Hi John; Welcome to Permies!
You have the basic idea right. They both use a small hot fire, heating a large mass.
One big difference is Masonry heaters are insurance company approved, (if built by an approved mason) Rocket Mass Heaters except in a few cases are not.
Masonry heaters have a mandatory second skin of brick for safety.
RMH's can but normally do not.
Rmh's however are not limited to just a barrel and a bunch of heavy mass.
The standard rmh that you have seen is known as a J tube design.
Newest RMH technology has moved on to what is known as a "batch box" rmh . These generally use an all brick vertical bell . Similar in appearance to a Russian masonry stove.
Here is a link to the best batch box information site.
http://batchrocket.eu/en/
Oh, one last difference. A proper masonry stove is around $10,000 . A RMH can be built for $200 If you bought new bricks and the best building supply's, MAYBE you could spend $800 - $1000
Check things out , here at Permies & over at Peter Bergs site batchrocket EU .
I think you will be impressed!