The original was “Ultimate Soundtracker,” and it was so influential that derivatives often named themselves ___tracker (noisetracker, screamtracker, impulsetracker)
The term probably arose from the naming, starting with the very first one: Soundtracker (1987) on the Amiga, obviously a play on the word soundtrack. From there we got Noisetracker, Startrekker, Protracker, Fasttracker (MS-DOS) and so on.
I can't say much about the early history, but trackers have a unique UI compared to other DAW software. Instead of a staff or piano-roll, the tracker UI looks more like a spreadsheet, with each column being a channel, each row being a step, and each cell containing a note or effect.
This representation meshed well with early demoscene music storage and code, and evolved into its own subculture in the late 80's and early 90's.
Ahoy on YouTube has a great video about tracker music, https://youtu.be/roBkg-iPrbw