There are two Pikes: Christopher Pike, Sr. and Christopher Pike, Jr.
Pike Sr. was born circa 2202 and is played by Mount in the Prime Universe and Greenwood in the Kelvin Timeline.
Pike Jr. was born circa 2220 and is played by Hunter in his only appearance in the Prime Universe.
Pike Sr. went to the Academy with Georgiou and we saw much of his record a couple episodes ago which included a stint as XO under April and official CO of the Enterprise between 2250 and at least until 2257. We don't know his ultimate fate.
Pike Jr. probably went to the Academy in the 2240s and was a junior officer, possibly XO (per rank braid) in 2254 when he was placed in temporary command of the Enterprise before Rigel VII and Talos IV. Pike Sr. was probably on Cardassia or something at the time. Pike Jr. does serve on the Enterprise in some capacity for 11+ years, and eventually reaches the position of Fleet Captain and hands the ship over to Kirk and then gets himself paralyzed and Talosized.
I mean, I don't believe any of this, and it's throwing all intent out the window, but why not?