Generally, yes. Most soldiers on a front were not transferred to other fronts unless there was a breakthrough on one side or the other. Germany was the only one, I think, which had opportunity and cause to shift troops back and forth, but to my knowledge, mostly kept troops in their theatre of origin.

The Eastern Front was actually very different from the Western Front. Much more mobile, a bit more bizarre. It’s certainly interesting to think of what veterans of the two fronts might have traded as compare/contrast!