Isn't it the case that there are a near infinite number of forms of cancer for any organ? Any combination of mutations that causes unrestricted growth right? So how can it just be 2 forms?
Likewise DNA is likely to break (and fail to be corrected) at particular points. Some of those points cause cancer, but there's only a finite set of those points since DNA is largely identical across all humans. Additionally, even if the failure is slightly to one side of the expected break, it usually shows the same symptom.
This doesn't sound even remotely true to me, except in the case of an absolute beginner doing the welding
In practice, we've now molecularly characterized most well-studied cancers and know that they tend to have the same mutations. For example, certain DNMT3A mutations are very common in AML and the BCR-ABL fusion protein in CML (and results from an interaction between chromosomes 9 and 22 that produces the mutant 'Philadelphia chromosome'). There are even a wide range of cancers that share similar patterns of mutations and fall under the umbrella of 'RAS-opathies', which all exhibit some kind of mutation in a subset of genes on a specific pathway related to cell differentiation and growth. Examples include certain subtypes of colon cancer, lung cancer, melanoma, among many others.
More generally, when a cancer is subtyped, that subtyping is always done with respect to some quantifiable biological trait or clinical endpoint and – as you've hinted – that subtyping is commonly a statistical assessment. Each cancer is unique and, even within an individual cancer, we have clonal subpopulations – groups of cells with differing mutations, characteristics, and behaviors. That's one of the reasons treating cancer can be so challenging; even if we eliminate one clonal population entirely, another resistant group may take its place. The implication is that cancers that emerge with post-treatment relapse are often 1. more or completely resistant to the original therapy, and 2. exhibit different behaviors and resistance, often to the detriment of the patient's outcome.
However, medicine is practical, and tries to draw boundaries where different therapies help differently or where there are different pathophysiology going on.
The article was able to draw a new additional boundary. Its relevance is yet to be confirmed with its phenotype or druggability. If it turns out to be useful either in predicting therapy or outcome, it'll stick and oncologists will learn it.
This process has already been repeated a lot in the hematological cancers, where previously cancers like "Hodgkin's lymphoma" have been subdivided as we made new treatments and discovered the individual pathways.