Second snail sounds like it could be a ramshorn. First is bladder/pond snail like others said.
Get rid of them ASAP unless you want a snail population explosion. Either manual removal, assassin snails or fish that will hunt them (loaches puffers etc) or make a trap. There are some good examples of snail traps kicking around here somewhere.
Or leave them in if you dont mind seeing them all over, which will happen unless they get dealt with when there's only a few.
Dwarf cichlids can eat snails and my snails were all over the tank before the corydoras went in and now are hiding. I caught a corydoras red handed with a snail in his mouth.
Plants grow, leaves die, snails and other herbivores eat the dead leaves, detritivores consume snail poop and make mulm, mulm feeds the plants. Circle of life.
Herbivore poop is large, carnivore poop small because of the amount of food the animal needs to eat to survive. Meats are much more nutrient dense than plants. Think how much material those snails are taking in to have that much waste, they must be doing a great job finding and eating debris in the tank.
dont worry about it other than not looking nice they are actually useful.
I have assassin snails like someone else suggested or if you have room you could get a Dojo Loach, or a small Clown Loach but with the Clown loach it will out grow your tank so you'll have to either get a bigger tank eventually or trade it in at your LFS but the Dojo would be fine just a little less common