There is one AOTC. It can be claimed by the student or the parents. If your parents claim you as a dependent, then they claim the credit only.
If your parents could claim you as a dependent, but don't actually claim you, then you can claim the credit in your own name, although you won't get anything unless you owe enough tax to use the credit (generally, your taxable income is more than $15,000). There is no "free money" for being a college student, except in the rare case where you are over age 24, or your parents are deceased.
In some cases where a parent's income is so high that it knocks them out of the credit, it is better to not claim the child as a dependent so the child can get something, rather than the parents getting nothing, but this needs to be discussed and some test tax returns might need to be prepared.
