What is the difference between a T-Carrier and a Digital Signal?
T-carrier describes both an electrical specification as well as the data layer. DS specifies only the data layer. There is a lot of crossover between the two naming schemes though. For example, any T1 you order from a telco today will almost certainly be a DS1 over HDSL or HDSL2; it's never a "real" T1, but everyone just calls it a T1.

A DS1 contains 24 or 32 64kbps channels. A DS2 contains 4 DS1s, along with some "slop bits" so that the individual DS1s don't have to be synchronized to each other. A DS3 contains 7 DS2s, or 28 DS1s. You will never find a technical paper saying that a DS2 contains 4 T1s because the electrical specification is irrelevant; only the signal description, the DS-spec, is used.