Some hosting companies advertize themselves as premium reseller hosting providers, what their difference from "reseller programs?"

What company do you mean?
As for me I use reselling from Ahosting.biz and they provide many features with in-house support.

Nothing special, just a term to call quality reselling.

What company do you mean?

They also offer domain registration.

I guess premium means they are using premium bandwidth providers, so that your reselling clients can enjoy maximum stability.
@Pontiy:
which bandwidth providers do ahosting.biz use? I heard they use Hostdime datacenter.

I think that the main difference is quality. In this case I would suggest you also
mmhosting.com
webhostingbuzz.com
Both are stable and premium reseller providers

Do they say they are Premium hosting providers? Or do they use premium network providers?

As I understand MMHosting.com provides NETbasic plan, they don't have a Premium one if you are talking about this company.
As for Webhostingbuzz.com they provide budget web hosting with free domain name for life.
Whta companies do you mean, Mirror?

Not sure about other companies, but I know that webhostingbuzz.com allows overselling on their reselling plans, how do they do this technically, I wonder?