While they don't all pick one over another, there are limitations on how available and consistent you can make systems, for the same level of partition tolerance - https://en.wikipedia.org/wiki/CAP_theorem

While technically you're right, the CAP theorem uses a very strict definition of availability, which is often not needed to consider the system available in real-life. Also the consistency in CAP theorem is defined as linearizability, and this is just one of very many kinds of consistency. Often the systems are ok with weaker types of consistency.

Therefore, I'd really like that everyone stopped labeling distributed databases as AP or CP, because this is an oversimplification and most of the time, just plain wrong.