Kyle is nails on...
DS3=Digital Signal level 3 (logical) = T3 Transmission level 3 or Technology level 3 (physical) depending on who you speak with.
A DS3 is also the equivalent of a STS1 Less the SONET over head and an STS1 (synchronous transmission signal)is the electrical equivalent of an OC1(optical carrier).

DS2= 4 DS1's. And I too, have only seen them on "low speed cards" in an M13 mux. They are pretty much only a logical entity. That’s probably why I don’t recall ever hearing them referred to as T2’s either.

As far as extending it, you need to use coax cable with BNC's (Bayonet Neil Connectors) only. Do not try to use "F-type" connectors that you would use for cable TV. However, RG6 cable should do just fine (two runs, one transmit the other receive). When extending it don't forget to check the line build out or you may run bit errors even if the cable is okay. You are better to over drive the signal a little, if in doubt.
Good luck! DS3’s are actually very easy to work with. Even easier if you have the proper tools and test equipment.

PS.
Don’t forget, 672 DS0’s ride a DS3 (24-channels on a DS1 times 28 DS1’s on a DS3=672 DS0’s (lines)). So, don’t unplug it at 4PM when everybody is making their last calls of the day or you’ll make lots of enemies.