From a certain point of view, it's Amazon using different terminology - what others call a data center, they call an AZ...or even a subset of an AZ, and we'll never know exactly - nor the capacity of each[0]. And what they call a data center, others call a region.
[0] When a server class is "sold out" in a region, you can't start your server - but there's no indication of this anywhere until you try to start your server. Other cloud providers auto-rebalance VMs to make space - using AWS is sometimes more like using physical servers than VMs - maybe moreso with paravirtualization.
I'm really confused as to what you're trying to say.
AWS has been very open over the years about what their terminology means. When they say datacenter, they mean it in the traditional sense of the word. When they say an AZ is made up of at least one but sometimes multiple datacenters, they mean that that an AZ has multiple physical datacenters. They're not slicing up a server room and calling these multiple datacenters.
We also know that AZs are physically separated from each other.
So an AWS region has at least as many physical datacenters as it has AZs, and potentially quite a few more.
James Hamilton has talked pretty extensively about this stuff at re:invent, and as an AWS customer, his talks have been some of the most interesting to me.
Other people calling a datacenter a region doesn't suddenly reduce an AWS region down to a datacenter. A datacenter is a word with a pretty specific definition, and an AWS region does not fit that definition.
[0] When a server class is "sold out" in a region, you can't start your server - but there's no indication of this anywhere until you try to start your server. Other cloud providers auto-rebalance VMs to make space - using AWS is sometimes more like using physical servers than VMs - maybe moreso with paravirtualization.