And sometimes you get a bit of both in one go, as with the May 2018 release of Leo Colovini's Fae from Z-Man Games, this being a redesign of the 2002 title Clans that keeps the gameplay the same while changing everything about the look and setting of the game.
In both games, five different colors of pieces occupy the spaces on the game board, with each player secretly representing one of those colors. Each turn, the active player moves all the pieces in one space to an occupied adjacent space, then if a group of pieces is isolated, it scores, with each color in the group scoring points equal to the number of pieces in the group. That's pretty much the game aside from nuances on moving and scoring. Once the game ends, players reveal their colors, possibly score bonus points, then see who's farthest ahead on the scoring track.
Much of the game comes from the bluffing that everyone must engage in, and your attempts to see through that bluffing. Can you set up a move that will help you more than an opponent? What's more, can you set up a move that an opponent will perform, thinking it's better for them than for you?
Colovini revisited this "hidden faction" gamespace in 2004's Familienbande, with each player in that game representing a genetic trait that's being passed down through the generations as players create marriages, then present the offspring of those marriages. Both games feature the Colovini trademarks of simple rules and a highly interactive shared playing space in which everyone's actions affect what others can possibly do. I'd say that Fae feels like a throwback to pre-Agricola days when no one bandied about the term "multi-player solitaire", but that's kind of like saying an old game is old — and as we all know, everything old is new again...