One is "legal" the other is "total problem space"
From a computing point of view, the total problem space is what matter because you still have to "compute" if it's legal or not before moving on. There isn't a straightforward way to only iterate over legal positions.
"no more than 218 possible next moves" would be a lot clearer...
> By checking all approximately 8.7x10^45 reachable chess positions?
That's a large overestimate.
https://github.com/tromp/ChessPositionRanking accurately estimates the number of legal chess positions at ~4.8x10^44.