I'm playing Fortnite on Xbox with an ordinary TV. Now that I get a 144hz monitor in a few days, I wanted to ask if the monitor makes the game run a bit smoother.
No, the game will run exactly the same.
Definitely not
The game does not automatically run smoother, you may see more fps, which means you see it more smoothly.
Xbox One, Xbox One S and Xbox One X should be able to output 120 Hz on suitable displays from May. There are also groups, simplified parental controls and video editing before uploading.
The other question is whether your monitor also supports this. If this is the case, you will definitely notice a difference.
Note: A new monitor does not increase the potentially possible frame rate from the PC.
If your PC can't calculate 144 fps right now, a 144 Hz monitor will not display them either.