Is there any difference between run command in terminal & ALT+F2

I don't think there is any difference between the two it's just that once you run a command using Alt + F2 the dash closes before you see the results / output. But it is used according to different purpose as following.

Use Alt + F2 when running commands that expected no output or that open an external application. Example: gksu nautilus which opens up a root nautilus window.

For commands that expected an output - ls,rm, find, update, upgrade, install, etc then recommended to use the terminal.

Yes! I originally said no because the differences are relatively none imo since the same binaries process the command in the end. That said CTRL+ALT+F# and the Quick-Run cmd are different virtual terminals so there are bound to be small differences, like the .bashrc file wont be loaded for Quick-run commands. So alias commands that you have set up wont work and such.