In the case of the Remote Execution/Cache API used by Bazel among others[1] at least, it's a bit more detailed. There's an "ActionCache" and an actual content-addressed cache that just stores blobs ("ContentAddressableStorage"). When you run a `gcc -O2 foo.c -o foo.o` command (locally or remotely; doesn't matter), you upload an "Action" into the action cache, which basically said "This command was run. As a result it had this stderr, stdout, error code, and these input files read and output files written." The input and output files are referenced by the hash of their contents, in this case, and they get uploaded into the CAS system.
Most importantly you can look up an action in the ActionCache without actually running it, provided you have the inputs at hand. So now when another person comes by and runs the same build command, they say "Has this Action, with these inputs, been run before?" and the server can say "Yes, and the output is a file identified by hash XYZ" where XYZ is the hash of foo.o, so you can just instantly download it from the CAS.
So there are a few more moving parts to make it all work. But the system really is ultimately content-addressed, for the most part.
[1] https://github.com/bazelbuild/remote-apis/blob/main/build/ba...