This controversy existed since 2002 when the NRS proposed a subtype classification of rosacea. In the later part of 2016 the RRDi has now endorsed the Phenotype classification of rosacea. This article remains to explain why this controversy existed but the subtype controversy is no longer worth debating since we have moved into this new direction in diagnosing rosacea into phenotypes, which has proved superior to the subtype classification. There is no controversy with the phenotype classification of rosacea. However, for those who want to learn why we have moved away from the subtype classification you may read the article below to understand the history.
In 2010, a report by the ROSIE [ROSacea International Expert] Group reports that, “Classification of rosacea into stages or subgroups, with or without progression, remained controversial.” This ROSIE group is comprised of “European and US rosacea experts.” Two of the experts in the group are MAC members of the RRDi, Dr. Draelos and Dr. Jensen. The report, was released by J Eur Acad Dermatol Venereol and said, "the ROSIE group proposed that therapy decision making should be in accordance with a treatment algorithm based on the signs and symptoms of rosacea rather than on a prior classification." This prior classification of rosacea into subtypes and one variant was released by the National Rosacea Society in 2002 by an 'expert committee.'  The ROSIE group report concluded:
"The group suggested a rational, evidence-based approach to treatment for the various symptoms of the condition. In daily practice this approach might be more easily handled than prior subtype classification, in particular since patients often may show clinical features of more than one subtype at the same time." 
This is not a new controversy. The late Albert Kligman, a noted expert on rosacea, stated in 2003 about the NRS classification of rosacea into four subtypes and one variant:
”In my view this is a vast oversimplification which will not solve the diagnostic dilemmas that confront us. I see no reason not to give equal nosologic status to granulomatous rosacea, rosacea conglobata, rosacea inversa (formerly called pyoderma faciale), rosacea fulminans, edematous rosacea (a devastating variety) or combinations with seborrheic dermatitis, lupus erythematosus, acne vulgaris, and still other variants. Reducing the classification to four sub-types does little to clarify and eliminate the inherent complexities of this mysterious disease.” 
Another report released after the ROSIE group report mentioned above had this remark about how a ‘proper standardization’ is needed:
“It is to be remarked that the quality of most studies evaluating rosacea treatment is rather poor, mainly due to a lack of proper standardization. For a major breakthrough to occur in the management of rosacea, we need both a better understanding of its pathogenesis and the adherence of future clinical trials to clearly defined grading and inclusion criteria, which are crucial for investigators to correctly compare and interpret the results of their work.” 
This controversy is simply because the NRS classification is based not on nosology but rather on morphology." Nosology (from Ancient Greek νόσος (nosos), meaning "disease", and -λογία (-logia), meaning "study of-") is a branch of medicine that deals with classification of diseases. Diseases may be classified by etiology (cause), pathogenesis (mechanism by which the disease is caused), or by symptom(s).....A chief difficulty in nosology is that diseases often cannot be defined and classified clearly, especially when etiology or pathogenesis are unknown. Thus diagnostic terms often only reflect a symptom or set of symptoms (syndrome)." Wikipedia
No doubt this controversy will continue until more is known about the cause of rosacea. What is the morphology of rosacea? Morphology in biology deals with the outward appearance (shape, structure, colour, pattern) as well as the form and structure as opposed to physiology which deals with the function of an organism. The NRS 'expert committee' said in its initial report on this classification of rosacea into subtypes and one variant:
"As knowledge increases, it is hoped that the definition of rosacea may ultimately be based on causality, rather than on morphology alone." 
So this was a start into everyone being on the same page when it comes to diagnosing rosacea. And the NRS 'expert committee' concluded in its report:
"This investigational instrument is intended to set the stage for a better understanding of rosacea and its subtypes among researchers and practitioners by fostering communication and facilitating the development of a research-based classification system. As a provisional standard classification system, it is likely to require modification in the future as the pathogenesis and subtypes of rosacea become clearer, and as its relevance and applicability are tested by investigators and clinicians. The committee welcomes reports on the usefulness and limitations of these criteria." 
The future is here and the ROSCO panel has moved the classification in a superior direction.  Since the jury is still out on what exactly is causing rosacea and the fact that rosacea's definition is still controversial amongst the medical community, we need to keep an open mind about what constitutes rosacea.
What is puzzling is that the NRS 'expert' committee excluded three rosacea mimics as variants of rosacea:
The committee has their reasons for this and said:
"The committee noted that certain disorders may have been prematurely identified as associated with rosacea or as a variant of rosacea, and for clarity should be recognized at this time as separate entities. There is insufficient basis at present to include the following conditions as types of rosacea."  The RRDi classifies these as rosacea variants. What is puzzling is the NRS absolutely makes no mention of demodectic rosacea as a rosacea variant, while the RRDi does.
In 2011 a new group of physicians have proposed a new subtype of rosacea called Neurogenic Rosacea.
A paper published in Europe had this to say about this subject:
"The classification of rosacea into stages or subtypes, without considering the possibility of progression from one to another, will probably remain controversial until additional knowledge on the pathophysiology of rosacea is obtained." 
So if in the future we learn that rosacea is caused by a single entity or by several different entities or in combination we might have a completely different classification system or one similar but based upon 'causality' rather than morphology. And most important is that we certainly need more knowledge about rosacea. Until then, diagnosis of rosacea sometimes results in misdiagnosis and continues to be mysterious and bewildering.
Dr. Frank Powell, at the 2012 annual meeting of the American Academy of Dermatology, is reported to have said that the subtypes in rosacea may be different conditions. 
In 2016, the ROSCO panel wrote, "The panel recommended an approach for diagnosis and classification of rosacea based on disease phenotype." 
“Given the overlap of rosacea features across subtypes and the fact that no single treatment completely addresses all rosacea features, the current approach of diagnosing and treating rosacea by subtype may hinder individualised patient management. A new approach is needed to bring us closer to helping each and every rosacea patient receive the right treatment according to their signs and symptoms.” Jerry Tan, MD 
“While the rosacea management landscape has advanced, the current subtype-based view of the disease can hinder progress by limiting the way we consider treatment options. These new ROSCO recommendations should help to make a positive impact on future treatment development and ultimately help improve the lives of people with rosacea through a symptom-led approach.” Esther J. van Zuuren, MD 
"The panel agreed on phenotype-based treatments for signs and symptoms presenting in individuals with rosacea." 
The ROSCO panel doesn't discuss rosacea variants.
RRDi Endorses the ROSCO Panel
 Rosacea – global diversity and optimized outcome: proposed international consensus from the Rosacea International Expert Group
Elewski BE, Draelos Z, Dréno B, Jansen T, Layton A, Picardo M.
J Eur Acad Dermatol Venereol. 2010 Jun 23.
Full Text Available
 Standard classification of rosacea: Report of the National Rosacea Society Expert Committee on the Classification and Staging of Rosacea
Wilkin J, Dahl M, Detmar M, Drake L, et al.
Journal of the American Academy of Dermatology April 2002 • Volume 46 • Number 4 • 2002;46:584-587.
 A Personal Critique on the State of Knowledge of Rosacea
Albert M. Kligman, M.D., Ph.D.
 Rosacea Treatments: What’s New and What’s on the Horizon?
Gallo R, Drago F, Paolino S, Parodi A.
Am J Clin Dermatol. 2010;11(5):299-30
 Clinical presentations and classification of rosacea.
Department of Dermatology, Venereology and Allergology, University of Duisburg-Essen, Hufelandstrasse 55, 45122 Essen, Germany.
Ann Dermatol Venereol. 2011 Nov;138 Suppl 3:S192-200.
 Research suggests rosacea subtypes may be different conditions
Dermatology Times, Dec 1, 2012, John Jesitus
 Br J Dermatol. 2016 Oct 8. doi: 10.1111/bjd.15122. [Epub ahead of print]
Updating the diagnosis, classification and assessment of rosacea: Recommendations from the global ROSacea COnsensus (ROSCO) panel.
Tan J, Almeida L, Bewley A, Cribier B, Dlova N6, Gallo R, Kautz G, Mannis M, Oon H, Rajagopalan M, Steinhoff M, Thiboutot D, Troielli P, Webster G, Wu Y, van Zuuren E, Schaller M.
 Br J Dermatol. 2016 Nov 12. doi: 10.1111/bjd.15173.
Rosacea treatment update: Recommendations from the global ROSacea COnsensus (ROSCO) panel.
Schaller M, Almeida L, Bewley A, Cribier B, Dlova N, Kautz G, Mannis M, Oon H, Rajagopalan M, Steinhoff M, Thiboutot D, Troielli P, Webster G, Wu Y, van Zuuren E, Tan J.
Edited by Brady Barrows