There are some great answers here, just adding a bit based off your recent edit.

"Evolution" is a great way to frame development of cancer cell lineages. For a cell to develop into malignant growth, it has to be able to "outcompete" neighboring cells to go from cellular expansion > avoidance of immune system > invasion of extracellular matrix > treatment resistance. One of the core concepts is the idea of driver mutations, where certain mutations are more likely to lead to further mutations hence "driving" to cancerous developments.

The infamous BRCA gene is one such example. If one person inherits a mutated copy and then develops a mutation in the other copy, they lose the capability to prevent damaged cells to undergo programmed cell death (apoptosis). When combined with other risk factors (female sex, radiation exposure, OCP use, etc.), random mutations can pile up that would normally be prevented by functioning BRCA gene products. Colon cancers also show a similar line of progression (APC > KRAS > p53 > VEGF genes) where the initial inherited mutation increases risk of developing cancers.

Another classic example would be the Li Fraumeni Syndrome, inherited dysfunctional p53 gene. The p53 protein is crucial to detecting damage to DNA and then initiating repair or cell death. Cells with one inherited mutated copy of this gene who further develop "non-hereditary" mutation in the other copy now lack this the capability for DNA repair in future cell divisions (two-hit hypothesis). Most of the time, other repair/immune mechanisms will prevent cells without a single functioning copy from turning cancerous; however, in cell lines that physiologically divide rapidly (skin cells, GI cells, bone marrow), cells can escape these mechanisms. Families with Li Fraumeni Syndrome can present with a variety of cancers in their medical history ranging from breast cancer to brain cancer.