By logic, a tweaked existing spell would be a homebrew spell, since a homebrew spell by definition is a non-[official content] spell, therefore a tweaked existing spell, which is not [official content], IS homebrew.
A homebrew spell is a non-existing spell that the character has developed with the ok of the DM (or that the DM has developed).
There are specific guidelines in the DMG (chapter 9).
Once the spell is created, sure it's homebrew, but it's an existing spell in the campaign world.
Using wish to create a spell "on the fly," that's not covered by ANY other spell effects from ANY spell lists (which is what you seem to be proposing) allows for HUGE versatility. That seems the prevue of the second part of wish.