Hello I have a medium voltage switchgear that has the following nameplate, hopefully that can be seen in the image or via the url
or here.

Can someone please explain to me why the the Integrated Switch and Fuse short circuit current is "better" than the momentary current and fault closing current? Someone was trying to explain to me that since the Integrated current is larger and that there is a fuse the numbers above or only 'applicable' if the fuse was not there. Is this right? How does this work?

It looks like the interrupter switch has ratings of:

61 kA Momentary Current
40 kA Fault close
25 kA for 2-seconds short time current.

The fuse has a 59 kA interrupting rating. Since it is part of the panel board assembly it's lower rating would supersede the switches' 61 kA rating, so you should be ensuring this 59 kA momentary/fault rating is not violated.

Further, the fuse clearing at 2 seconds is about 550 amps, so the two second rating of the switch will not come into play .. at 25 kA the fuse will operate long before the 2-second limit for the switch is reached.