That's precisely what it is, yes. This is one of the (extraordinarily few) lessons the 5e designers did, in fact, actually
learn from the design choices of 4e. I can't really call this one a "mistake" because it was fully 100% intentional for 4e. They wanted to reward tactical (re)positioning and forced movement of enemies. 5e, on the other hand, is not, and the designers wanted to pretty heavily shut down forced movement as a behavior for players. You'll see references to this in a variety of spells.
Of course, what you're asking for here is exception-based design, which the 5e team all but explicitly rejected because it smelled too much like 4e.
That is what natural language does. It doesn't actually
explain anything. This is what 5e--both 5.0 and 5.5--has always had on offer. And the people cheered.
I mean, I think one can draw a useful distinction: willing vs unwilling. "Entering" refers to willing motion. Instead of "moved," since that's already pretty loaded, how about "propelled"? Then "move" is just a generic term for any kind of motion (forced or willing), "entering" can only be done willingly, and "being propelled" happens regardless of the recipient's intent.
Of course, 4e already had stuff like this, it's essentially keywords again, so of course 5e fans will shout it down. Can't have big bad WotC telling you how to play!