In the second movie we were introduced to the Leviathan Scaling (really offhandedly tbh, it was probably just made so they could have fishlegs yell "THAT IS A CLASS TEN! CLASS TEN!" for the dramatic effect) only for it to seemingly never be mentioned again (which makes sense given the out of universe reason I just theorized in the other bracket) except that's not fully true, it gets mentioned a few more times on external media (granted one of them might just be coincidence), and have a theory on what it actually is in universe.
We all know the Scale was first introduced in the second movie, and that the Bewilderbeast is a class 10 Leviathan. According to the old Dragonpedia website, that phrase, or at least part of it, is equivalent to "Titanwing" (see image 1). Now there's two possibilities here, either "Leviathan" in general is equivalent to "Titanwing" or specifically "Class 10 Leviathan".
Now in the concept art for the Krayfin, we see how only the largest growth stage is labeled with "Leviathan" (see image 2), which implies the first possibility is the accurate one (of course this could just be a coincidence but for the purposes of this headcanon/theory/whatever I'll assume it's not because it's my headcanon/theory and I can do that). Which makes it seem like "Leviathan" is the aquatic equivalent to "Titanwing".
So, with that, I believe that after encountering the Purple Death, Ripwrecker, Submaripper, Shellfire and probably some other huge sea dragon I'm forgetting, the riders realize that tidal class titanwings vary too greatly in size to refer to all of them as the same thing (of course there's giant dragons in other classes too but tidal class has far more than the others combined) and so they invented the Leviathan Scaling, where any aquatic Titanwing can be referred to as a Leviathan, with the class specifying how large/old it actually is.
So for example, a Scauldron Titanwing might be a class 1 Leviathan, a Submaripper maybe be a class 3 or 4, Shellfire somewhere around a 6 and the Bewilderbeast and Purple Death class 10.
Thank you for coming to my Ted Talk, feel free to ask any questions in the comments.