Rice flour is ground from long- or medium-grain rice, the same kind of rice that most of us probably have in our pantries. It has some thickening properties, but is better used in gluten-free flour mixes for baked goods.
Sweet rice flour is ground from short-grain glutinous rice, aka "sticky rice." Don't worry, though; the fact that it's called glutinous rice does not mean that it contains gluten. Rather, this rice has a much higher starch content than other kinds of rice, making it an extremely efficient thickening agent for sauces or binder for things like mochi and noodles.
And don't let the fact that it's called "sweet" rice throw you off either. It's flavor is mild and almost milky, not at all sugary sweet. Look for this flour labeled as mochiko in Asian groceries.
Sweet rice flour ended up working perfectly in our bechamel. How do you use these two flours?
Related: What's the Difference? Soba, Udon, and Rice Noodles