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These terms are not precisely defined in engineering conversations.
Originally, they were base band voltage waveforms with specific protocols that were used on cables that originally carried FDM analog telephone signals. They were optimized to carry the same number of telephone signals, only digitized.
Today, they can also mean a portion of a digital stream at the same bit rate but is sent over microwave or fiber optic links. These bits can be of ordinary data and not telephone conversations.
T1 is about 1.544 Mb/s and E1 is about 2.048 Mb/s so you cannot go from E1 to T1 if the E1 is running at full capacity.