I don't know of a difference.

But I caution you to not do the power rake thing in moist soil, as the grass may just pull right out of the ground. Best bet would be to let it get growing this spring, mow it to about 1 to 1.5" and then power rake: that will let the debris set up on top of the nap of the lawn, where you can easily rake stuff up and get it out of there.

If this is part of a 'kill it and reseed it all' project, go ahead and do the power rake a week after roundup is applied.

Same machine.

As you probably already know, an aerator is different. But, I think a power rake and dethatcher are just different terms for the same machine. Some lawnmowers call an attachment a power rake, but, that is all together different then what most people think of when they use the term about a piece of equipment.

Dethatcher, Power Rake, and Vertical Mower are all the same machine.

Power rake and detatcher are NOT the same thing. A power rake is far superior to a simple dethatcher which only rakes up thatch. A power rake will take up 2-3 times more thatch than a dethatcher attachment. Google power rake to find out what it is.