The speed of the animation (Camera movement moving objects) will depend first on how fast they move in the scene, Sometimes you could confuse because of the speed you see in the viewport but this doesn't nessesary display the actual camera/object speed, you need to do preview render to check the actual camera speed. Viewport performance will vary depending of size of scene and hardware.
Once you get your camera/object animation at the correct speed, then you choose your output FPS, in theory, if you render the same animation, at 24 FPS or 30 FPS they should look the same 'speed', what it changes is the clarity of the animation, one may create more motion blur than the other one if this is activated; animation over all would look more smooth.
If you render at 60 FPS and play at 60 FP the speed of the animation would be the same, but you get more detail on the visuals, less motion blur. If you play those 60 fps rendered frames at a lower Frame rate, then you get the slow motion effect, without skipping frames.
If you render at 30 FPS and play at 24 FPS you'll get similar effect but not that noticeable. If you render at 24 FPS and display at 30 FPS you'll get skipping frames, animation becomes choppy. The same if you render at 30 FPS and play at 60 FPS.
In resume changing frame rate after recording or rendering animation is not a random exercise, you only can do it with limitation, to create a special effect of visuals. Otherwise, you'll get undesirable results.
If you want your animation to move slower, you need to render is at a slower peace (more frames over all) not FPS but how many frames are used to object X to move to the next position.
Hope this help you.
Cheers.
