No, they are not the same thing. A UTI is a bacterial infection of the urinary tract. Interstitial cystitis involves an inflammatory condition in the lining of the bladder. I've read a few different theories as to what the cause is so far, so I can't comment on that, but I know that once damaged certain foods, supplements, inhaled chemicals, etc can cause pain.
Many treatments for a UTI could cause severe pain in someone with IC. For example, garlic, ascorbic acid, and cranberry juice are very bad for people with IC, but are helpful in treating a UTI.