Correct, the differences make the analogy good enough to visualize the concept. It does however suffer from the same problem as the balloon one, in which someone can get the impression the expansion has a center. The wiki for the expansion of the universe goes through the various analogies and where they break down.

I would suggest Dr Becky's Youtube channel for a number of excellent videos on the expansion as well as the current problem of getting an accurate measurement of the correct Hubble expansion rate. The James Webb telescope was hoped to solve that dilemma, but we still aren't sure.