For the memory "mismatch" Task Manager shows the "Private Working Set" Memory usage of a Process, Process Explorer by default shows Private Memory Usage.
My understanding is that the difference is largely that Task Manager indicates how much Physical Memory is being used, whereas Process Explorer will show how much memory it has allocated, including memory that is in the pagefile.
So for example right now I have Firefox showing 1.1GB usage in Process Explorer, but about 900MB in Task Manager, because about 100MB was swapped to disk.