As I understand it, it also adds long guns to that, though I’d like to be wrong on that.
It requires you to get the same (or a very similar) license to purchase a long gun from a private individual, but long guns are not subject to registration by the Michigan State Police. Once you get the license, you sign it, the seller signs it, then you each keep a copy and it's done.
If you buy from an FFL you don't need to get the license from the police or sheriff. A purchase record will be provided by the FFL, just as they do now for handguns.
They didn't think this law through, which is true of most of these knee-jerk gun laws. They require you to have a license to transport a long gun within the state, but they also grandfathered all existing long guns and won't require you get licenses for all of the ones you already own.
So how are they to know that the gun you have in your trunk was before or after the license requirement?