In principle, yes, in practice, no; real-world mutations are (more often than not) non-random and their frequencies can be affected by a variety of factors. For example, the location of the mutated gene or region within the bundled chromatin structure inside the cell nucleus (this structure is highly conserved into what are known as topologically associated domains, or TADs), or the interaction between a region of DNA and cellular machinery that increases the likelihood of some mutation. There are tons of examples.

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.