Why are you asking?
I’m guessing it’s because you’re the sort of person who just enjoys knowing things and not because you’re trying to open up your DVR, copy the files off it, and play them on your computer. Because that would be against your customer agreement, and we don’t talk about that sort of thing on this blog.
So let’s agree it’s just for entertainment value.
The files on your DIRECTV or DISH DVR are stored in the same MPEG-2 or MPEG-4 transport stream that’s used when they come from the satellite. The file formats are not terribly different from DVD and Blu-ray disc files, really. That’s not what makes them special. The special part is the multi-step encryption that’s needed to decode them. With DIRECTV DVRs, the files are encoded not only at the source but also with the individual ID number of the receiver. It may not be impossible to crack the encryption, but no one’s done it yet. With DISH, I suppose it’s “theoretically” a little easier since the recordings are not inexorably tied to the receiver, but it’s still so tightly coded that no one’s cracked it.
If you were to open up your DIRECTV DVR — and you should not do this — and mount the drive on a computer capable of reading a Linux-formatted disk, you’d find a fairly predictable file structure and you’d find many large files that are very obviously recordings. They’re not labeled “This is Us” and “Scandal” because that’s just not how DIRECTV does stuff. But it’s going to be obvious that they’re video files because they’re just so darn big. You could, theoretically, copy them to your hard drive…
…and then nothing would happen. You couldn’t play them, you couldn’t use them in any measurable way, they would just be sitting there taking up space. That, my friends, is the miracle of encryption.