These are not two names for the same system. One has the rope already above you. The other has you placing gear and feeding a lead rope. Mixing the kits is how people cut a sheath or take a factor-2 onto a start anchor.
The distinction
Top-rope solo — the rope is already fixed above you. You track it with progress-capture on your harness. See Top-rope solo.
Lead rope solo — you start from the ground or a belay and lead upward, clipping protection, with a self-belay device on your harness. See Lead rope solo.
Manufacturer box
Petzl treats fixed-rope self-belay as its own problem and recommends two independent captures. Self-belay on one or two fixed ropes. GRIGRI / NEOX remain unauthorized for self-belay. Notice.
When each system is the wrong tool
No fixed line above you is not top-rope solo. That is lead rope solo, or you walk away.
A progress-capture on a slack lead rope can cut the sheath. That is not a lead-solo belay.
One grab and no backup is not a TR-solo system.
Partner-belay GriGri orientation on your chest is not a lead-solo path.
Next checks
Other systems this page assumes or hands off to.
Lead rope solo — Harness-mounted self-belay on a lead rope: anchors, HUUD path, backups, multi-pitch labor.
Top-rope solo — Fixed line above you, two independent captures, and why this is not lead solo.