If you have AA miles you must spend with AA and are subject to AA t&c’s for awards.
If you have AS miles you must spend with AS and are subject to AS t&c’s for awards.
If you have BA avios you must spend with BA and are subject to BA t&c’s for awards.
With redeemable miles/points/avios in an airline frequent flyer program you can spend(use) for an award flight on that airline and the airline frequent flyer partners of that airline.
Each ffp has different rules & costs (in miles and cash co payments) for awards.
Frequent flyer miles/avios/points are not equal to earn or use.
You cannot move miles/points/avios from one ffp to another ffp
Awards are not guaranteed to be available a when you want to travel. You need to be flexible on dates & routes