I typically consider the thin red line the classic Reid Headwall. Start on the cone, cross the bergschrund, traverse to the gully over the weird fin, finish in the left gully and try to thread the rime shroom. You can, as has been said, start anywhere and climb anything in between.
Blue line is Leuthold's. The "obvious" rock at the bottom is the biggest clue. But the first time I did Leutholds I did the Reid. This is made more confusing since you can follow the base of the blue, then follow that ramp up to the gullies, since it's lower angle. But the red line is a lot of fun.