Both mean stories, possibly true, possibly untrue, carried by word-of-mouth--one person telling another, who tells another.
"Scuttlebutt" is literally a nautical term, although most people don't know its origin. On sailing ships, it was the barrel used to store drinking water. Sailors would meet and chat while getting water at the scuttlebutt, in exactly the same way as they now meet and chat at the watercooler at work.
"Scuttlebutt," then, means casual rumors and information, on any topic, spread by word of mouth. A related idiom is "I heard it through the grapevine."
At work, someone might say "Well, the scuttlebutt is that the raises aren't going to be very good this year."
"Gossip" generally means "dishing the dirt," telling unpleasant stories about peoples' personal lives, generally their love lives. For example, in the United States, there is a story in the papers about the President maybe, or maybe not, having had an affair with a woman named Stormy Daniels. Basically, that's gossip.
This picture by Norman Rockwell, "The Gossips," illustrates the spreading of gossip. I don't know if these facial expressions are universal, but in U.S. culture just from the faces we can guess that they are talking about something shocking to some, amusing to others, and disreputable... and it is even possible to guess that it probably is about something scandalous having to do with sex.
https://tinyurl.com/y96yq58x