Will a transmission out of a 01 Monte fit a 2000 Monte?

 

Yes, it will.

 

Not necessarily.
The large bold letters that run vertically on the ID tags have to match, otherwise differences in the internal electronics will make them incompatible unless you use the PCM and TCM from the donor car. There were three different variations of the 4t65e in both 2000 and 2001.
ID. tag:

Here's a quote from Dave at Triple Edge Performance: http://www.tripleedgeperformance.com..._App_List.html