Are dolby digital and AC-3 the same?

Dolby Digital comes in a few flavors: 2.0/5.0/5.1/EX6.1. AC-3 is the older term for the Dolby Digital format and you normally won't hear that term used today. Any DVD that indicates Dolby Digital will be supported by your receiver. DTS is a digital 5.1/ES6.1 format but not Dolby Digital. Most likely your receiver only supports Dolby Digital 5.1 or less. DTS DVDs normally have a Dolby Digital option that allows your receiver to play DTS DVDs.

I have always been under the impression that AC-3 is the term for the general encoding scheme, and that DD is a specific type of encoding under that scheme. Actually, with all the different "flavors" of DD, it's several different specific types of encoding under the general scheme. In any case, Yes, your receiver will decode the output of your DVD player.

I thought that DD used data compresion and DTS rearanged the data to fit like a puzzle. Eliminating the need for compresion which degrades the signal.

As it was explained to me DD uses about 11/1 and DTS uses about 4/1 -compressions.