Wolf3D used raycasting, rather than tracing to give a pseudo-3D rendering of what was basically a 2D grid map.
It's pretty clever how it worked, I remember having a LOT of fun cooking up my own similar renderer back in the day (Turbo Pascal with inline asm was fun!). If I remember rightly:
First, the ceiling and floor were drawn in, covering everything (intersecting in the middle, vertically). Then, they took your location on the map, and cast a ray for each row of pixels (320 of them, I believe). This ray went forward until it intersected a wall - and the distance to the wall was measured. It then did a quick calculation (lookup table) to determine the height of the wall at that distance, subtracted half that height from the center of the screen, and plotted a vertical line in the color of the wall. I seem to remember the wall color was retrieved from a small texture and scaled.
That gives surprisingly good results, albeit with no lighting or shading.