Everything will be off if the game settings do not match the actual monitor resolution except possibly in a few rare situations, maybe. Much is determined by that.
You are saying that you set the GAME resolution to 1080p, not the monitor resolution, right? Because unless you have a configuration that allows you to use a virtual resolution, I'm not sure how you'd even do that. Personally, I'd recommend the game resolution be set the same as the monitor.
Anything else could potentially create visual or performance issues.