What is Half track and quarter track?

I used to own a 4 track Dokorder reel-to-reel machine back in the '70s & '80s. I had 4 meters that I could engage all at once, or choose which track I wanted to record on. I never did much with this feature because all I used the machine for was to record my LP's. What the heck is a quarter track and half track machine? Do they use the same width of tape that a two track or 4 track machine would use? Are half track and quarter track machines for consumer use or just for pro use? Were pre-recorded tapes two track?
A half track used the entire width of the tape to play or record; a quarter track used half the width of the tape and so would play or record in both directions. So half track used twice the tape quarter track did. All prerecorded tapes I ever had were quarter track; half track was for pro use or serious amateurs. They are the same as two track and four track, half track means that it used half the tape to record one channel and half the other, so it was called two track. Quarter track used 1/4 of the tape to record one channel of the music, you went to the end and then reversed the tape to get the other two tracks. So quarter track and 4 track are the same.
Quarter track allows you to record 4 tracks on a quarter inch tape or two stereo tracks in both tape directions. Half track literally divides the quarter inch tape in two. A wider track and all things being eqaul, beter signal to noise due to a wider track but, you can record in only one direction unless you have a need for half track mono. Many decks especially pro units had both a quarter and half track head and allowed switching between heads depending on the tape being played back.
Hifigy, I didn't see dualhead Studers, Revoxes or Tandbergs on ebay. This must be custom version, I suppose.
The Technics RS1500 series was a quarter inch, two track machine for recording and playback. However, it also would play 4 track tapes via a switch on the head block. Great machine and is the choice for Tape Project restorations.
Mitch, the machine you are referring to was when 4 channels were in vogue. I had a Phase Linear 4000 preamp that was 4 channel. The recorder you had could record 4 channels in one direction. It was called "Quadrophonic".