This is a difference between 'spend' (you have to have) and other key words. Yes maybe they could be explained better, but once you realize that, it makes more sense. Give it another try.

Simple enough:
Remove is "discard/lose as an effect". The cost is playing the card and using up one of your slots for the round. But other cards you can get later and/or in other decks say "spend" instead of "remove". Those are "discard/lose as a cost". (that said, life is always* remove, not spend... because if you don't have enough, remove takes what you do have anyway... which kills you and causes you to lose the game. Spend would just fail.)
*to the best of my knowledge.

If you've not seen these things happen enough to notice the difference, you've probably not been playing for That long... that or you've really not been paying attention.

Mind you, the game does have a few issues (spend X of card type Y from your hand choses which cards of that type to take from your hand At Random... Why?! And, of course, the inevitable bugs from time to time.) but calling it stupid is a fairly massive overstatement.

Semantically speaking, ZetaNicco, you are right. Both "remove" and "spend" mean that something that once existed is now gone.

In this game, "Spend a weapon, gain 5 gold" means that the latter action is a condition of the former. Without a weapon being spent, you get no gold.

In the same vein, "Remove weapon, gain 3 gold" SHOULD mean that if there is no weapon to be removed (condition), there should be no gold gain. You cannot remove something that does not exist.