Well, most use them interchangeably and although I can't go into detail on what each one is made of, I can give you a little info on them. Soft hand clear is used more for a "fashion" type look to soften the cured ink to more match a waterbased ink. I've found that soft hand will greatly reduce an ink's opacity if not careful. Reducer is the one I dislike the most and I think it's misused the most in our industry. It's plasticizer and most inks are close to their max with plasticizer already so you risk overloading the ink. Reducer will increase flash times, cure temp, reduce opacity, increases after-flash tack, and increases build-up. You really don't want to use reducer on inks that have hardened (aged up) because there is physically no room for them to mix in with the resins and blend properly. Extender base is used a lot of time for black (or dark inks that don't need opacity and/or will be printed alone) inks so shops can extend a gallon of ink with a ton of extender base and turn it into 2 gallons really quickly. I don't know what extender base and soft hand clear are made of, possibly resins/surfactants/plasticizers...maybe someone will chime in with that info.
