You are right, I was oversimplifying. For example, Wikipedia lists 4 more frequent types of brain tumors, and each of them has subclassifications. The origin of the cancer is important, because the cancer cell retain some properties of the original cells, for example if they are affected by hormones. So location is important to distinguish if it started as a breast or skin cancer, but it's not important to distinguish if it started as a hand or foot cancer.

(After metastasis, the location is not important to understand the properties of the tumor, but it can affect the symptoms.)