Hi there, welcome to IronWorks.
No, it doesn't. If a weapon is, say +1, +3 vs Goblins, then it gives +3 bonus to THAC0 and damage against Goblins and +1 to everything else, not +4 against Goblins.
And no, you're not being stupid.

Some AD&D rules and descriptions can be a bit confusing for newcomers to the game. I know it took me personally a long time to sort out everything.