When we refer to playing "both sides" of a tape, it is somewhat of a misnomer.
All program material is actually on the same surface of the tape, just that it may be contained on a different portion of the surface.
Full track mono : The entire widththe tape is used on a single pass. This would be comparable to driving on a single-lane one-way road.
1/2 track mono : 1/2 of the width of the tape is used per pass. After recording on the first "side", the tape is "flipped over" and run through the deck again, recording on the other half of the tape surface. Comparable to driving on a two-lane road, one lane in each direction.
1/2 track stereo : 1/2 of the width of the tape is used for each channel, with the entire width of the tape being used in a single pass. Comparable to one side of an interstate highway with both lanes traveling in the same direction.
1/4 track stereo : 1/4 of the width of the tape is used for each of the two stereo channels per pass. When the tape is "flipped" or reversed, the other portions of the tape is used. Most common configuration is tracks 1&3 in one direction and 2&4 in the other. No good highway comparison that I am aware of.
1/4 track quad or multitrack : 1/4 of the width of the tape used for each of 4 channels of recording, all at the same time and/or in the same direction. Popular for discrete 4-channel recordings during the time of "Quad". Also can be done on a machine such as a Teac 2340 or 3340 unit. Was popular for small studios and home recording.