The main difference is the pulse width. TENS is not supposed to contract muscles, and employs lower widths. EMS contracts muscles and employs longer pulse widths.
The theory thread explains the role of pulse widths, and how it relates to the chronaxie of the muscle. Generally TENS goes up to 200 microseconds, whereas EMS needs to go up to 450 microseconds. TENS only need to excite pain nerves (nociceptive neurons). EMS need to excite motor nerves. There are also other differences, like on/off (work/rest) cycles, but in general TENS, given their goal to mask pain, and because they do not contract muscles, can stay on continuously. There are other secondary effects, but the above are the main ones.