Multimedia "texts" are actually MMS. In fact, if you send more than 160 characters, those are also MMS because it's an extension of the SMS standard.

https://en.wikipedia.org/wiki/Multimedia_Messaging_Service

It is not unusual for there to be hosting or intermediate storage of images and other files, and from the phone you may tap a link or something to download/access that file, instead of having it automatically download and appear immediately, due to bandwidth and resource constraints.

Aren’t SMS that are over 160 characters being concatenated? There used to be a standard for that.

Generally yes.

I guess a phone/app could exist that does convert to MMS instead, though, since the app can make that decision.

In France, I'm "charged" for MMS, too. But that's actually considered "data", so it's deducted from the "internet" envelope which is quite generous (at least for my needs: I have multiple dozens of GB for under 10 € a month, of which I only ever went above 10 when backing up photos during a vacation with no wifi).