However, Doom also renders textures using an algorithm that sort of paints walls as like vertical lines of sorts. The exact algorithm it uses makes it hard to look up (to pitch), and I think impossible to roll the camera. See <https://en.wikipedia.org/wiki/Doom_engine#Rendering> — it has a good animated graphic of what happens if you do look up, and the differences between the output of Doom's software renderer's algorithm and something actually rendering 3D.
¹modern ports have ways to accomplish this, and even before there were direct ways of doing it, clever map layout and instantaneous teleporting can get pretty close.
Raycasting (in gaming, some graphics folks just use it as another term for raytracing) means to fire a ray for each column of the screen, identify where it collides with a wall, and use that to determine what to render for that column - it's basically per-column raytracing.
DOOM's engine instead uses a BSP tree so that, from any position, you can determine which walls are on-screen instantly just by walking the tree - the nearer walls appear earlier in the traversal than farther walls. It's still column-based (it tracks whether each column has been drawn and won't draw further walls behind an already drawn column, and stops drawing once all columns are filled), but there's no rays cast.