No difference - just different names for the same thing. It's not uncommon to hear people switch between referring to them as either stones or rocks, since both terms are widely-used and interchangeable.
"Rock" is probably the more popular term in the U.S., while "stone" is probably more popular in Canada.
"Broom" and "brush" are also interchangeable. "Brush" is not used much in the U.S., more so in Canada. Neither term is really too fitting anymore, though, since most curling brooms are now made with a rough synthetic fabric covering a foam pad, rather than the more traditional horse hair or straw bristles.
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