It's not about the size of the tape width. I believe the reason it is not just called a two track is because there used to be a lot of two track reel to reel stereo decks made, that used a quarter track format. That meant you could record two tracks at a time, but be able to turn the tape over and record two more tracks in the opposite direction. Each track used a quarter of the tape width.
Those were called 1/4 track stereo decks.
A 1/2 track, 2 channel (stereo) deck, could I guess, be made using any tape width, but 1/4" and 1/2" tape widths are the most common.