Do some helicopters require classes, type ratings, or special endorsements, the way some airplanes do?
I can't see a connection between "classes" of helicopters and ratings.  

You also don't specify which jurisdiction so I will answer for the UK CAA which I know.

To fly any helicopter under VFR needs nothing more than your license, gained on any type, and a type rating for the specific aircraft.

For example, I gained my license on the R22.  I am therefore also type rated on it.  The second aircraft I learned to fly was the B206 which is jet powered.  I didn't need anything extra than the appropriate type rating.

I can fly any helicopter for which I am rated under VFR.  If I had an IFR certification, I could fly any helicopter I am rated for under VFR, and any IFR certified helicopter for which I am rated under IFR.

"Difference training" is simply part of the the type rating.  For example, if I ever learned to fly a craft with a retractable undercarriage, I would be rated to fly that type, but not another type with retractable gear.

What does differ is the type of license, e.g. CPL or ATP.  I would need that license in order to carry passengers for hire and to conduct other commercial operations, but I still need a type rating on whatever helicopter I use to carry those passengers.

Put it this way, the day after I gained my license, I could climb into any helicopter and act as pilot under training.

Hope that's all clear!