ATMega328P-PU and 328P-AU
The -AU and -PU suffixes on the part name indicate different packages. The former is used for the "32A" package (32-lead TQFP), and the latter is used for the "28P3" package (28-lead DIP). In plain English, the -AU is a surface-mount part, and the -PU is a breadboard-friendly chip.

As far as functionality, there is virtually no difference. The 32A package exposes pins for ADC6 and ADC7, which are not available on the 28P3 package, but they are otherwise identical. (Note that these pins are only used for the ADCs; they are not a member of any port, and thus cannot be used for digital I/O.)