The refresh rate is the amount of frames your display can show per second. The unit for this is Hertz (hz). This is 60hz on the Steam Deck. This is an engineering thing and there isn’t too much you can do to change this.
The framerate is the amount of frames your graphics card produces per second. The „unit“ her is often fps (frames per second).
You cannot exceed the 60hz limit of the Steam Deck‘s screen since it is a hard limit, you would need to build a new screen into the Deck. So optimally you want your GPU to produce 60 fps or more to use the display to its full extend.
Smoothness is a little harder. You can have a game with 60fps on a 60hz screen that still feels choppy because the timings are misaligned. Imagine your GPU produces 59 frames in half a second and then only 1 in the other half. Your screen would freeze for almost half a second because there is no new frame arriving at the display for half a second. Here you have to look at your frame times. They should be as consistent as possible.
So to sum up: refresh rate = times your monitor can show something new (hard limit)
fps = frames your GPU can produce per second (you can change that via the settings of a game)
frame times = the time a frame „waits“ on your screen. (The shorter and the more consistent, the better)
Sometimes lower fps seem more fluid than higher fps because the fewer frames are arriving more „punctual“.
This is kinda true. In my opinion there is no point in locking the fps to 60 when you could also be getting 90 fps on a 120hz screen. Might as well use those frames as long as they come in regular intervals.
The lower the fps / hz the bigger the intervals between frames and refreshes and the more noticeable the stuttering and lag. If you exceed consistent 60 fps it should all feel roughly the same. There is no need to get an expensive 240hz screen to game at 100 - 120fps. 120hz or 144hz is enough for that. (As always depending on what you do with it, a professional CS player might need the higher Hertz)