The more natural expressions would be “have a family” or “start a family” I want to have a family someday. Let’s start a family. (Let’s have kids) Build or make could be ok in certain contexts but they’d be rare in regular speech.

They are essentially the same.

I would say build a family is more formal because it doesn't connote 'make', ie sexual intercourse! If you give a full sentence it's easier for context...