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If they are planaria, they are basically detrivores (trash eaters) but would eat any fish eggs and could potentially crawl onto and harm sleeping fish. If you look at them with a magnifying glass they look like the drawing in the link below. The two big dark eyes that look sort of crosseyed are confirmation you have planaria. Feeding only the food your fish eat, cleaning the aquarium and filters will reduce the number of planaria to the vanishing point. Additional filtration and aeration will help too. A hydrogen peroxide dosing system will gradually wipe them out but not harm fish or live plants.

There is NO such thing as gravel worms.

do you have a filter or a air pump?

If you do then the filter or air pump could be pushing and moving your fish's poop around.

fish poop varies from brown to white.

If your that worried get a gravel pump ( hand pump - 10$ electric pump - 40$ ) from pets-mart.

and do 25% water changes also. also make sure you use water conditioner ( stress coat ) and artificial bacteria (stress Zyme )

Keep your fish tank healthy so your fish can be healthy. If you are worried about poop then get some catfish ( peppered cory catfish ) which eat poop and leftover flakes off the gravel in your tank.

you overfeed, and don't vacuum your gravel properly.

if you feed way way less, like 5-10 times less food

and use a siphon cleaner gently to remove more filth and less water during your water changes

then the problem will go away.

It's a symptom of rising waste levels, and a real threat is that a bunch of the worms will die suddenly and pollute the tank almost instantly.