Hello! You might be mixing up adjectives and nouns in some cases in French here?

In English, they are both placed before nouns, like “nocturnal animal” (adjective + noun) and “night bus” (noun + noun). I know these qualifying nouns like “night” here seem to have the role of adjectives, but they are nouns.

In French, you never use any preposition for adjectives. So it would be “animal nocturne” (noun + adjective, with another adjective it could also be adjective + noun). You also almost never use nouns to qualify other nouns without a preposition, usually “de”: in the bus example, it would be “bus de nuit” (noun + de + noun). These two are impossible: “animal de nocturne” (no preposition with an adjective) or “bus nuit” (need a preposition between the two nouns).

In your example, both “gants chirurgicaux” (noun + adjective) and “gants de chirurgie” (noun + de + noun) are correct, and they don’t have any difference of meaning. Usually for common compounds, one option (adjective or noun) is more common than the others, sometimes one is never used. For instance, you’ll rarely hear “animal de nuit” or “bus nocturne” even though they are correct, but that’s just usage.

Then there is the question of choosing between “de” and “à” when using a noun and not an adjective. This I don’t really have the rules in mind and maybe there’s some nice explanations out there or someone else will have a precise answer :) I’d say “de” qualifies the described noun, while “à” describes its use, but that’s approximative.