They are one of the planorbid snails - a tiny species of ramshorn.
Your zebra snails will be nerites and possibly the spotted snails as well (there are other snails with spots besides nerites). Nerites cannot breed in fresh water. They can and do lay eggs which look like sesame seeds stuck on the tank walls and decor but they don't hatch. Even if they did hatch, they'd hatch to a larval stage which needs to be in salt water to survive.