How is brain tumor different from brain cancer?

Brain cancer spec: Brain cancer is a specific type of brain tumor. Brain tumors are graded from grade 1 (benign) to grade 4 (cancer). Hence, brain cancer is a specific sub-type of brain tumor.

It may be the same: A tumor is abnormal tissue that is growing in an area where it really shouldn't be found. Tumors can be benign (such as meningiomas) or malignant (such as glioblastomas). People could use the term brain tumor to refer to either of these disease. Brain cancer would most often refer to only the malignant types of tumors or to cancer that metastasized to the brain from other sites in the body.

...: Brain tumor means any lump growing in the brain. It would include non-cancers such as meningiomas, and cancers that spread from elsewhere in the body, known as metastases. When we talk about brain cancer, we usually mean true cancers that started in the brain, such as glioblastoma.