The rules seem simple don't they? If you have natural nails, use acetone nail polish remover; if they are acrylic you have to use the non-acetone removers. I'm here to say, "Not true!"
Let me start by saying that I have acrylic over my natural nails, so you will know...this is what I do. Now for why that is not true. First, nail salons not only use acetone remover, they use 100% acetone on all types of nails. The second reason, non-acetone remover is weaker than water.
My recommendation: use the regular acetone nail polish remover regardless of what type of nails you have. Used normally (in other words, don't soak your nails in the remover), the acetone remover will not harm your artificial or natural nails. If you are concerned about the exposure to acetone, wear a latex glove on the hand holding the cotton with remover. So why do I have non-acetone remover? For removing glitter from my nails using the foil method (the directions are here).
I do suggest using a cuticle cream or oil and lotion on your hands after removing nail polish. All types of removers can be hard on our skin. Happy polishing!