It's a confusing area:
According to the "
Included vessels" list, both the Carrack and the Aquila should have an Ursa, suggesting that you should have 2 "real" Ursa's in your hangar in the game
According to the "
loan matrix", the Carrack receives a "loan" Ursa, while the Aquila does not have any loan items listed, which would suggest that you should have only a single ship providing a "loan" Ursa in your hangar in the game.
At the top of the "Included vessels" page, it does state that the "loan matrix" is what the game currently works with, which would suggest if you were to CCU from the Carrack to another ship, you would lose the rights to the "loan" Ursa that it provided and so would not have access to an Ursa despite owning the Aquila still...
As far as I know, those who have a pledge Aquila (and no other ships that provide a loan Ursa) still get the "loan" Ursa, though, which appears to indicate that there is a hybrid system in place that uses the "included" list for some ships (constellations with their snub fighters, for example) and the "loan matrix" for others.