That's because the Number one in Discovery IS the same Number One from the Cage. Well different actress of course. Discovery ties in with TOS as its a few years prior to it.I found an interesting thing today about Discovery, Pike and a homage to the pilot episode 'Cage' in the original series. In Cage, Spock wasn't first officer. Pike's second in command was a female officer known simply as Number One, in the same way that the first officer under Pike in Discovery is.
https://en.m.wikipedia.org/wiki/The_Cage_(Star_Trek:_The_Original_Series)


