The T-Carrier System was developed by Bell Labs. Bell Labs developed a series of systems for AT&T, some of which were actually used. According to Dr. John Pan, who worked for Bell Labs:
"The story of the 'T' in T1 has its roots way back in 1917, when AT&T deployed the first carrier system, called the A-system. A total of 7 A-systems, providing four voice channels over an open wire pair, were ever deployed. Then came successive analog frequency division multiplex systems named B, C, D, and so forth. Few of these carrier systems ever saw commercial service. AT&T, being a monopoly, could well afford many dogs. A notable success is the L-system, providing 600 (L1) and later 1800 (L3) voice channels over a pair of coaxial cables, in long haul service from 1944 to 1984, until the breakup of the Bell System forced AT&T to migrate to optical fiber. The last of the analog carrier system is the N-system and its variants, providing 12 voice channels for intra-city short haul. Along with the even more forgettable 'O', 'P', and 'U' systems, the emergence of 'T' killed them all.
"In 1957, when digital systems were first proposed and developed, the boss decided to skip Q, R, S, and to use T, for Time Division. The idea was this will be the world's first time division system. Interestingly, except for 'U', another system that never made it, this naming system ended.
"Variants of T1, called T1C, T2, T3, and T4, all died. They are survived by signals that would have been carried on all these systems, called DS1, DS2, DS3, and DS4.
"Among the successors to T1 vying for success at Bell Labs, digital coaxial cables, digital microwave, satellite, circular waveguide, optical mirror, and optical fiber, none achieved commercial success save fiber."
The designation "DS" refers to "Digital Signal" and describes the physical layer. The designation "T" refers to the type of carrier that is being used. Often these are used interchangeably but that technically is not correct. The Physical layer focuses on the electrical characteristics such as signal shape, voltage levels, etc.
The basis of the T-system is the DS0, which is a 64 kilobit-per-second data stream. A voice conversation is sampled 8000 times per second, and each sample is one byte, or 8 bits, long. However, the T-System is unbiased, it treats voice and data equally (since voice is really just data).