CAP is basically a continuum along which BASE and ACID are on opposite ends.
CAP is Consistency, Availability, and Partition tolerance. Basically you can pick 2 of those but you can't do all 3.
ACID focuses on Consistency and availability.
BASE focuses on Partition tolerance and availability and throws consistency out the window.
In theoretical computer science, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store can provide only two of the following three guarantees:[1][2][3]
Wikipedia