There are two digital technologies both of which fit two voice channels into the 12.5kHz bandwidth normally occupied by an analogue radio channel.
Both use a frequency modulated FM system (like most analogue voice radio systems) although it is a slightly different modulation scheme called Frequency Shift Keying FSK. In practice this means RF propagation, Aerials, Duplex Filters and other external RF parts are identical to Analogue FM radio systems.
Both systems are available in licensed and licence-free equipment (which is similar to the PMR446 specification).
DMR - Digital Mobile Radio. Wikipedia DMR
This technology first transmits voice channel A at the full 12.5khz modulation then Voice channel B in the same way, A,B,A,B,A,B etc. So the channel is shared on a time basis. (This method is called TDMA). This is of course happens at a very fast rate undetectable by the radio user.
Advantage: DMR allows the use one Repeater to repeater two voice channels.
dPMR - Digital Private Mobile Radio. Wikipedia dPMR
This technology splits the 12.5khz into two 6.25Khz channels which transmit simultaneously. A and B. This method is called FDMA
Advantage: In theory range should be better than DMR because the same transmit power is spread across half the bandwidth.
Disadvantage: Two repeaters are required, one for each channel.
Both of these technologies are supposed to be an Open Standard to allow equipment from different manufacturers to be interoperable. In practice this probably holds true for basic voice communications.
Signalling and other data dependent features such as GPS are often propriety restricting use to a system closed to all but one manufacturer.
Compatibility across technologies
Currently most (if not all) digital radios will also work in analogue mode so can be set to talk to analogue radios as well.
DMR radios will not talk to dPMR radios and vice versa.