Yes, there are subtle differences.
If the game runs at 60 fps and you're recording at 60 fps, you're exactly copying the visual appearance of the game.
If the game runs at more than 60 fps and you're recording at 60 fps, the game is generating more frames than OBS is able to capture for a 60 fps video, so some frames are left out.
If the game is running at a multiple of 60 fps, for example at 120 fps, or 180 fps or 240 fps, every other frame is picked (or every third, every fourth, depending on the actual multiple). This appears as smooth 60 fps video.
If the game is not running at a multiple of 60 fps, it depends on the ratio of recording fps and game fps which frames are picked. If the game runs at 70 fps, for example, and the recording with 60 fps, most of the frames are picked and every 7th frame is dropped. Since it's not a constant time distance from every frame to the next frame, the recording looks a bit stuttering due to to this, not as smooth as the original game, and not as smooth as if the game would run at 60 fps.