[3.5 or PF] Prone and movement.

[isildur]

Prone: A prone creature is lying fl at on the ground. Any
creature, even a limbless one such as a snake, that can fl atten
itself on the ground can choose to be prone, even if it can’t reasonably
be tripped or knocked down. An attacker that is prone
takes a –4 penalty on melee attack rolls and can’t use ranged
weapons aside from crossbows and shuriken. A defender that is
prone gains a +4 bonus to Armor Class against ranged attacks,
but takes a –4 penalty to AC against melee attacks.
Standing up is a move action that provokes attacks of
opportunity.

there is no mention about moving.
In pf, there is Rogue Crawl (Ex)

Benefit: While prone, a rogue with this ability can move at half speed. This movement provokes attacks of opportunity as normal. A rogue with this talent can take a 5-foot step while crawling.

But there is no "normal" line.

[Lord Vukodlak]

Prone: A prone creature is lying fl at on the ground. Any
creature, even a limbless one such as a snake, that can fl atten
itself on the ground can choose to be prone, even if it can’t reasonably
be tripped or knocked down. An attacker that is prone
takes a –4 penalty on melee attack rolls and can’t use ranged
weapons aside from crossbows and shuriken. A defender that is
prone gains a +4 bonus to Armor Class against ranged attacks,
but takes a –4 penalty to AC against melee attacks.
Standing up is a move action that provokes attacks of
opportunity.

there is no mention about moving.
In pf, there is Rogue Crawl (Ex)

Benefit: While prone, a rogue with this ability can move at half speed. This movement provokes attacks of opportunity as normal. A rogue with this talent can take a 5-foot step while crawling.

But there is no "normal" line.

See Actions in Combat

"Crawling

You can crawl 5 feet as a move action. Crawling incurs attacks of opportunity from any attackers who threaten you at any point of your crawl. "

[Chronos]

But nothing says you can crawl while prone. With what I think of as "crawling" and what I think of as "prone", you can't: Prone means your body is against the ground; crawling means you're on your hands and knees.

[Lord Vukodlak]

But nothing says you can crawl while prone. With what I think of as "crawling" and what I think of as "prone", you can't: Prone means your body is against the ground; crawling means you're on your hands and knees.

Nothing in prone says you can't move either, being on your hands and knees clearly isn't standing up. And you can crawl without being on your hands and knees its possible to drag yourself across the floor. Ever heard the phrase crawling on your belly like a worm.

Furthermore in PF a crawling character specifically called out as being considered prone, and while Wizards Rules of The Game aren't actually considered rules they also say you can crawl while prone.