Priority doesn't exist. It isn't a thing. Stop acting like it is because you are wrong. Ground moves clink, aerials trade. The only things that matter with regards to disobeying these rules are transcendence, invulnerability, super armor, and if an attack deals 9% more damage than another one.
..."Priority" does not refer to a literal value on a hitbox. In some games this actually happens (usually for projectiles) but this is rarely what anyone
ever means when they mention it. It considers not only startup frames, but actives, hitbox size, hurtbox size, invincibility frames, ect ect. It's more of a concept, or a tendency, not necessarily a "value" or a specific "flag" that pre-determines what move wins.
So, everything you mentioned has to do with priority. It doesn't exist
to you because you don't know what you're talking about. It's a very simple concept and you should, but again, i forgot i'm on the Smash forums where simplistic concepts are either debated for no reason or take alternate meanings.
EDIT:
Also, there's nothing "ambiguous" about frame data. It's about as objective and straightforward as it gets, actually.
The statement "good frame data" alone is quite ambigious.
When you say "Toon link has better frame data", you are not only omitting which attributes are good and why, but other key factors like the size and positioning of said hitbox...quite relevant information when you're discussing 2 characters where one of
the biggest differences are the sizes of their hitboxes and hurtboxes. (And if I want to be cheeky, i can also go ahead and mention, it's ignoring damage, base KB and KBS as well.)
Granted, it's much easier to conflate "fast startup frames" to "good frame data" in Smash 4 because on-shield offensive attributes are trivialized. So things like blockpush, blockstun and shield damage can be more or less ignored except for
very specific characters, and the only things that really matter are how fast it comes out, how far it reaches and how fast you can act afterwards. So if we weren't talking about Toon Link and Link i wouldn't have even quipped.
Case in point, Shiek's amazing Fair would be less destructive to the cast if it had the exact same frame data but a much smaller hitbox area, or if her hurtbox extended farther. This would allow a wider variety of aerials and ground normals to either trade or outright defeat it, with its startup, active and recovery values untouched. Bonus Trivia: this would also reduce its priority! See how that works?