The concept is very similar, a fast burning fire heats a large mass and radiates the heat back over many hours.
Very cool. But also very expensive.
Yes, I've heard of them referred to as masonry heaters, too. Nice link. And yes again, especially when built professionally, or with stone, they are very expensive. I've heard that DIY stone kits are in the $10K range. For just the kits.
They are such different animals. When fire windows in a RMH were discussed, several folks said the window makes a less efficient burn, which leads to the possibility that these masonry heaters are not quite as efficient as a regular RMH. (Only in part, I suppose. I think there are many more differences in how they burn as well.)
Another primary difference is that the exposed barrel in a RMH provides more instant warmth for a room than the fire window in a masonry heater. Many traditional masonry heaters have a fire door that is not a window, so there is even less instant warmth. Some folks like to cob over their RMH barrels, for more of a masonry look, but again, that instant heat is lost, though you perhaps have a bit more mass-stored and released (long term rather than instant) heat in the masonry-style or masonry heaters.