Doom Marine armor represents events of Doom, while the Arena armor represents the backstory given for the characters in Arena.
According to Tom Hall, the Doom Marine is the descendent of William J. The game also establishes that Doom Slayer is the same character from Quake Arena/Live, but also the original Doom Trilogy/Final Doom/64. Canonically Quake Champions is a prequel to Quake III Arena. And is thus only known in Quake III Arena and Quake Live. As she only appears in Quake III Arena and Quake Live (canonacity to the Doom series is unknown), Crash does not appear in any Doom game. She is the only bot who does this, giving the impression of talking to the player.
The bot has a auto taunt program that every time you say something to her she says something random back. The match against Crash is an easy one needing the first to five frags to win.