I thought about this more after lecture, but if we're drawing lines with thickness, aren't we really just drawing polygons?

(Since, as mentioned in lecture, lines can't really have thickness)

Yes I think that's correct. Going along these lines, it seems like once the line has a certain "thickness" we would no longer be able to use Bresenham's algorithm to directly draw the line. Perhaps we could take the four vertices of the line (rectangle) and apply Bresenham's a couple times and then use the boundaries of the upper and lower lines formed from pairs of vertices to fill in the contents of the rectangle (or other polygon).

But drawing polygon has different requirements. We can also break polygon into triangles and draw them. Some algorithm also takes extra care making the lines look smoother, which would be different if its thickness is different.