Seems everyone has a different idea as to what generation grip modules are which. First of all Sig does not call them Generation anything. That came from the shooting community. But for arguments sake, we will call them Gen 1, 2 and 3.
The P250 started with a Gen 1 grip (2007-2009) then went to the Gen 2 (2009 to 2016). The P320 started with a Gen 2 grip (2014-2016) and is now on the Gen 3 (2016-????).
They are not called P320 grip modules. They are called P250/P320 Grip modules. There have been three major versions or Generations.
Otherwise you would have to call them "Sig P250 Gen 3 grip module/P320 Gen 2 grip module".
Yes, the Gen 1 grips had P250 on the front dust cover. indicating that they where for the P250 only. Well so did the Gen 2 grip modules at first. Sig either did not know they where going to make another gun that used the same modularity as the P250. Or they kept the development of the P320 close to the vest very well.
Somewhere along the lines. Sig replaced the P250 mold mark on the dust cover with grip make and size. Example, COMPACT MEDIUM.
Now I said 3 major revisions. I consider the first model Carry Grip module to be a Gen 2. But, it does not have the full rail on it. It has three slots instead of the customary 4 the compact grip has or the 5 the full size has. It now appears they are making the Carry Grip modules in Gen 3 format.
The next sub category could be the Sub Compact grip module. They made this in Gen 1, and Gen 2. During the Gen 2 production, they added a version with the rail on the dust cover.
Here is a example of mold marking changes.

The one with P250 is a Early Gen 2. The one with COMPACT MEDIUM is a late Gen 2.
This is a Gen 1 grip module. They used different magazine base plates as well have having a narrower front dust cover.
Gen 1 on the left and Gen 2 on the right. See the different style rail.
This is a OD Gen 3. It has the raised Slide Release fence. Also sporting some Talon Granular grips. No mold markings on the dust cover.
This is a quick and dirty post. I didn't feel like bogging it down with pictures. I know there will be many who will disagree with me. They will call it heresy and blasphemous. But what do I know. I just collect these little plastic things.
Flame Suit ON.