I'm a U.S. native speaker.
I do not recognize a difference in pronunciation between the two words. I say them exactly the same way myself. I do not normally notice a difference when I hear them. However, the word "currant," the fruit, is not a word I hear very often--it doesn't come up much in conversation. It exists but is not common in U.S. cuisine. Raisins are common, currants are not.
ahdictionary.com is showing me "kûr-ənt, kŭr-" for BOTH "current" and "currant," i.e. it is not showing me any difference.
Food names, incidentally, are an area where there can be regional differences in both vocabulary and pronunciation.