Perhaps this image (thread) represents the difference somewhat well:
The white lines are 2d and connect 3d coordinates through projection, no matter how far from the camera the coordinate is in 3d, the lines are of the same thickness:
The bottom bit is closer to the camera, yet the line is as thin as the top one.
Imagine the red arrows are what you refer to as 3d lines. Their size changes with perspective and with the distance to the camera. If you moved the camera very far away, those arrows would eventually disappear. The white lines will still be visible as they were even though they would describe a shape taking less space on the screen (because their 3d coords say so)
This goes back to the beginning of this conversant, a 2d line projected from 3d coords:
You can connect 3d coordinates with a 2d line.
Easy test with the HUD class:
Punch in crazy high numbers in one end and observe how it behaves.