CBTC is moving block because it just obviates the need for fixed block wayside equipment. Fixed block signalling just detects if a track segment is occupied, but in CBTC the trains can directly talk to each other, at which point blocks are superflous.

Both types of systems can be automated. And yes they do often coexist, like i mentioned in my grandparent comment. But brand new rail lines that install CBTC often don’t, to simplify maintenance; trackside equipment gets exposed to pretty hard operating conditions and can’t be fixed without some kind of shutdown of the rail line.