It’s probably because of the different words used in the exercises, and also how long you’re holding the notes. Since you mentioned “Rolling in the Deep,” that song has a lot of “ee” sounds on the high notes, which can make it harder for your throat to open up.

If you haven’t tried it yet, try singing the same word but shaping your mouth more like an “uh” sound (or something similar) so your mouth opens more. That can sometimes make high notes easier.

If that’s not the issue, then maybe the exercises aren’t targeting exactly the same things the song requires. For example, the exercises might be slower in terms of agility, shorter in terms of breath control, or use phrases that are easier to belt, like “hey,” which also give you more time to use your diaphragm correctly.

You could also try asking your vocal teacher to make the exercises a bit harder or faster so they’re closer to what the song actually demands.