It can be a little confusing. You can have 'digital radio' which can be heard via Sky Dig, Freeview, Dig Cable etc. These are radio channels broadcast via a digital platform. Some of the channels will be available on normal AM/FM/DAB, some not.
DAB stands for (I think) Digital Audio Broadcasting. This is radio that is transmitted over the air to a DAB receiver. You can get these for your home, car etc. There is no other way to hear digital radio proper.
As for which has better sound? Depends really. It's all about how much bandwidth is used for each channel/multiplex. To fit more radio stations on DAB, the existing ones are compressed more and more. The quality can then suffer. It's the same with Sky Dig, Cable, Freeview etc. I find that a perfect analogue signal on both TV and Radio is better than most digital channels.
The one advantage of digital is the extra information that can be carried with each channel/station.
I don't half talk rubbish sometimes!