Remathilis
Legend
I mostly think it's a colloquialism to distinguish them from the shorter 1-2 level tops modules of prior editions. I personally prefer WotC's "storyline" terminology.
Waterdeep: DH and Waterdeep: DMM do have links beyond both occuring in Waterdeep, and even to a lesser extent so does Tales of the Yawning Portal.
That is really the only 5e AP that has interested me so far.
Minor beef: I wish people would stop calling Wizards of the Coast's adventures "Adventure paths". They are adventures - big ones, certainly, but still adventures. A path consists of many steps - the only thing they've offered so far in print that I'd consider an adventure path is Tyranny of Dragons (though a two-part path is pretty slim). I'm not sure I'd consider Waterdeep to be one - as I understand it there's no real connection between Dragon Heist and Dungeon of the Mad Mage other than both being linked to Waterdeep.
I dunno, Storm King's Thunder seems pretty solidly in the AP mode. You have to defeat each giant type before progressing to the final destination. Same goes for Princes of the Apocolypse - why wouldn't that qualify?
I guess I'm not seeing the issue here. A really big module is an Adventure Path - as opposed to a single adventure which is one and done.
While they provide threads, it is also super easy to take most any chapter from SKT and use it without the original context and make close to no changes. It's more like a bunch of old fashioned modules given a suggested structure than a railroaded path. More of an Adventure Buffet.
You can also do that with any AP as each one is designed to also be used by itself if the DM so chooses.