Unlicensed is a game that was released when the console was at retail but wasn't licensed by the company. Homebrew is a game that was released, mostly likely at "Home", after the console left retail. I think it should be left as is as this is a nice way of differentiating between the two.
But what about games like Jay & Silent Bob's Mall Brawl on the NES? That saw a full on professional release by an actual company. That's far from a homebrew. And a ton of "in the day" Atari releases would fit as homebrews by definition. Maybe there shouldn't be a distinction at all?