PAE = Physical Address Extension. This means the CPU really has 36 address bits instead of 32. How do you get those extra four bits? You use the MMU. The addresses you use in your program are VIRTUAL addresses - they are translated into physical addresses by the MMU. The problem is that the CPU is still using a 32 bit pointer, so you get a max of 4 GB of space to address. Even worse, normally a program is only allowed to use 2 GB out of that 4 GB of space. The rest is reserved to the Windows kernel. Using something called 4GT (4 Gig Tuning), you can access up to 3 GB out of the 4 GB.
Suppose you need more than 3 GB. That's where AWE comes in. AWE = Application Windowing Extensions. This is a throw-back to the old EMS days on 16 bit PCs. This is good old-fashioned BANK SELECTING. You tell Windows to make a bank inside your 3 GB of space, then tell Windows to switch in and out banks of memory in that bank of space. With AWE, you can access that full 36 bits of addressable RAM (64 GB), but only a piece at a time inside that smaller bank.
