Mission Control behaving differently with monitor plugged in
This is due to the differing amount of spaces shown in Mission Control, and both situations can be re-created with independently of the quantity of displays.



When you have a small number of spaces, it shows like this:



When you have lots of spaces, it shows like this:



This is not due to the number of displays you have connected but rather simply the number of spaces you have open.

To recreate…


You can make it act like the first example by having a small number of spaces, and it will use the default size and show the name of the space.
You can make it act like the second example by having a lot of open spaces, and it will reduce the size of the space thumbnails to fit them on, and hide the space name if necessary.