You are correct that
The Movie version of GOTG do not contain any characters of Avengers, Fantastic Four, or Spider-Man.
The Comic book version does contain Vemon a spider- man friend / villian that was in one of the spider-man movie. The female Captain Marvel was one time the leader of the Avengers. Tony Stark ( Iron Man) join the team for several months. GOTG leader Starlord is dating Kitty Pride of the X-Men ( the same character in the xmen book and movies). finally a former GOTG member Angela is gonna be reveal as Thor sister. Drax is father of MoonDragon (Avenger).
So while the movie version will contain no mention of the Avenger / X-men/ Spider-man or the members GOTG origins, Each Members of GOTG has connections to all Marvel Family in the printed books.
that was something new added in the new version.
last volume they never had such combinations.
Infact the original team was pretty different. (compared to the movie)
Groot talked fully for example.
anyway.. original team post-annihilation:
Star Lord, Groot, Rocket Raccoon, Mantis, Love Bug, Gabriel (Uni Power wielder) and Deathcry (Shi'Ar)
Then evolved into another team as some members got killed (Gabriel and Deathcry) or left (bug).
For example, during the Universal Church saga (War of Kings saga)
It was: Star Lord, Rocket, Groot, Gamora, Drax, Adam Warlock, Mantis (not very active) , Moondragon, Phyla Veil and Cosmo.
Then added Major Victory and Jack Flag and then Bug again.
They also teamed constantly with other groups, like NOVA PRIME (NOVA) and QUASAR during the epic Cancerverse Saga.
Only in the new iteration they added Avengers (Iron man and then Venom) and multiuniverse displaced creatures ( Angela )
and briefly teamed with the X-men to rescue Jean grey.