What do you need to do?
A dex is organised by creature, which only helps if you already know the name of the one you want. If you are stopped by something, you know the obstacle instead. Start there.
What is still missing everywhere, including here, is how long each one takes to obtain. That is what we are measuring.
And what else they can do
Those three are the Pathfinding abilities — the ones that clear something in front of you. There is a second list, Mobility, and it is the bigger of the two: 19 abilities across 50 Aniimo, against traversal's three across 36.
The two are kept apart in the game, and the line between them is not always sharp — Hookshot is described as pulling you to walls or enemies, which sounds a lot like getting past something. Which of these open ground and which are decoration is nowhere stated, so this page does not rule on it. It says who has what.
How many Aniimo actually clear something
36 of the 86 in the dex carry a traversal ability at all, so a little under half of everything you can catch is, for map purposes, decoration. Those 36 hold 39 abilities between them, because 3 of them carry two — Celestis, Fahloo and Erlath — and one Aniimo covering two obstacles is one slot in your party rather than two.
30 of the 36 can be caught in the wild. The rest have to be evolved into, which is a real distinction when you are stopped right now: a creature you can go and find this evening and a creature at the end of a chain are not the same answer to the same question, and the pages above put the catchable ones first for that reason.
The dex grades these, and nobody explains the grade
Each ability comes with a level — a creature that does two of them reads like "Fly Lv.3 Swim Lv.2" — and 3 grades are in use across the 86: Lv.1, Lv.2 and Lv.3. Every page here now prints it, because a reader choosing between two Aniimo should see everything the game bothered to record.
What it is not is an explanation. Nothing anywhere states whether a higher grade clears an obstacle a lower one cannot, covers more ground per use, or only moves faster, and those are three different games. We are not going to pick one and present it as fact — that is the kind of confident sentence a wiki fills up with and then nobody can tell which half is real.
Why this is not just the dex again
Plenty of places list what each creature can do. What none of them tell you is how long it takes to get one. When two creatures both clear the same obstacle, that is the only thing that decides which you should chase.
It is a real decision, not a hypothetical one. Two Aniimo can clear the same water and be a weekend apart in effort, and the one described everywhere as the obvious pick is frequently the one that took whoever described it a very long time to get. An obstacle-first list is only half an answer while the other half — the cost — is missing, and it is missing everywhere, here included, until there is a game to measure.
That comparison needs a measured acquisition rate, which is the one thing this site has and nowhere else does. See how we measure it.