Is cancer still considered to run in a family even if every person who got it has a different kind of cancer?

Yes: There are several familial syndromes that can have variety of cancers associated with them. Thus even though different cancers are involved they still can be inherited.

Cancer syndromes: Yes- can be a syndrome within a family- even with different type of cancer being diagnosed. There are groupings of cancer seen more frequently together. See your doctor for details and what diagnostic testing /screening needs to be done and at what age should you start.