Gossip was the act of spreading unfounded or unconfirmed rumors around during idle conversations. It could be done with malicious intent or innocently. The grapevine was a term for a series of gossiping people whose conversations eventually made their way through a larger group of individuals.
In 2365, Jean-Luc Picard commented to Wesley Crusher that he did not want his cardiac implant condition becoming Starfleet gossip. (TNG: "Samaritan Snare")
In 2369, Quark told Odo in his bar that the grapevine said Miles O'Brien and his wife Keiko were having problems in their marriage. (DS9: "A Man Alone")