More precisely: partitions in the graph theory sense rarely (if ever) happen. In practice it looks more like a complete graph losing some edges.
Let's say you have servers in DCs A and B, and clients at ISPs C and D. Normally servers at A and B can communicate, and clients at both C and D can each reach servers at A and B.
If connectivity between DCs A and B goes down there is technically no partition, because connectivity between the clients and each DC is still working. The servers at one of the DCs can just say "go away, I lost my quorum", and the clients will connect to the other DC. This is the most likely scenario, and in practice the only one you're really interested in solving.
If connectivity between ISP C and DC A goes down, there is no partition because they can just connect to DC B.
If all connectivity for ISP C goes down, that is Not Your Problem.
If all connectivity for DC A goes down, it doesn't matter because it no longer has clients writing to it, and they've all reconnected to DC B.
To have a partition, you'd need to lose the link between DCs A and B, and lose the link from ISP C to DC B, and lose the link from ISP D to DC A. This leaves the clients from ISP C connected only to DC A, and the clients from ISP D connected only to DC B - while at the same time being unable to reconcile between DCs A and B. Is this theoretically possible? Yes, of course. Does this happen in practice - let alone in a close-enough split that you could reasonably be expected to serve both sides? No, not really.
Partition tends to be a problem between peers, where observers can see they aren’t talking to each other.
In the early days that might have two machines we walked up to seeing different results, now we talk to everything over the internet. We generally mean partition when one vlan is having trouble. One ethernet card is dying or has a bad cable. If the entire thing becomes unreachable we just call it an outage.
Iow: You can have CAP as long as you can communicate across "partitions".