There are three die types:
all have different signature bytes which may or may not impact loading code into them. Generally tho the programming software needs to know which part type is being used, at a minimum for installing bootloader code. Serial downloading may end up ignoring the signature bytes of a bootloaded part.
They can be had in different packaging, this is what Digikey is showing as available options:
-PU - 28 pin DIP
-AU - 32 pin TQFP
-AN - 32 pin TQFP
-MM - 28 pin leadless package, smaller than 32 pin leadless
-MN - 32 pin leadless package
-MU - 32 pin leadless package
-15AZ - 32 pin TQFP, rated for a higher temperature range
-15MZ - 32 pin leadless package rated for a higher temperature range
Any letters to the right of those seen when ordering indicate the method they are supplied - loose parts, parts in a reel, parts in a tube, etc.
Anything else is either an older part that did not follow the convention, or is a counterfeit part.
Tables 38.7 and 38.8 lists these options for the 328 and 328P for example, with H indicating a type of lead finish, and R indicating Tape & Reel availability:
And 328P options:
With these rated to 105C
I think you need to pull up the Automotive data sheet to see the Z numbered parts.
And the PB is a different data sheet as well.