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!