Unity movement and jumping

Should i use different script for movement and jumping in unity or is there better way do all the movement in same script. I am using character controller for the player in my game.

Short answer: Yes

I personally like to organize my scripts in a way, where I can deactivate every “mechanic” individually (like jumping, climbing, vaulting etc.) to have a better testing experience. So, yes, I did that and I would recommend doing that.
There might also be people that might consider it unnecessary to make another script for a few lines.

I dont know if there are any major differences in scripting when working with a character controller, but I dont think so.