They're synonymous. "Linker" is from Old English (so-called "Anglo-Saxon") and "connector" is from Latin. "Connective" is another form (from the Latin adjective) of "connector" (from the Latin substantive noun). They each have their own subtle nuances, but in the context you've given, they are all referring to the exact same thing. Now, if we were discussing a word like "given," I would be inclined to call it the past participle when used as such ("he's given me a present") and call it the "passive participle" in a passive construction: "The award is given to a different teacher every year." That's just my preference -- most people would just use the term "past participle" for both cases, even though they're clearly different. I would likewise use different terminology for the various uses of "would" (future of the past, conditional, polite request, past frequentative). I believe words should be chosen based on how well they communicate your message to your intended audience.

Although I read on grammar for other languages, I don't read English grammar texts so I can only give you an educated guess here. There are two possibilities. One is that linguists don't agree on the best term. The other possibility is that one term (e.g. connective) is the technically correct term while the others are simply descriptive. That is, a word that connects is indeed a connector and a word that links is indeed a linker whether those are the "official" terms or not.