Region, AZ, data center
A region has minimum 2 data centers.
Data center is physical location. 2 data centers are physically isolated.
Each AZ is backed by 1 or more data centers.
Abstracting things further, to distribute resources evenly across the zones in a given region, Amazon independently maps zones to identifiers for each account. This means the us-east-1a availability zone for one account may not be backed by the same data centers as us-east-1a for another account.
2 AZ within a region can talk to each other through private link in a fast way.