Have you ever had a dog that sort of kind of knew a trick? I think it's like that.
If your companion is trained to do something, they'll do it cause the GM is a fan of your character, the end. The only thing getting in the way of that is a hard move (miss or golden opportunity), cause to say no otherwise is lame and your GM shouldn't do it if they're any good.
If your companion isn't trained to do something, well, that's a golden opportunity. I mean, obviously right? If my dog isn't trained to keep out intruders, I'd be in the shit if I left my dog to guard my house, ya know? In the same way, if your companion isn't trained in a thing, the GM is welcome to make a hard move.
What that means is up to you, the GM, and how you interpret the fiction.
A companion not trained in Labor probably doesn't like carrying loads -- they'll shrug off your belongings and you'll discover they ditched your lantern at the worst possible time. A companion not trained for Travel tires quickly, and the GM will tell you about how it twists an ankle or you make bad time.
The training is exactly like the weapon tags -- they're convenient excuses to remind the GM what kind of hard moves to make when the opportunity presents itself. They're there to stop the GM from going "uuuh uuh so NINJAS ATTACK!" when we all know that's stupid, and your horse probably just lost a shoe on the rocks.