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They are more like application-specific terminilogy of the same process. DMT is more for fixed-line applications on baseline frequencies. OFDM is targeted for wireless applications with high frequency modulation.
There are several differences that emanated from the difference of channel these two waveforms are deployed in. discrete tome multi frequency (DTMF) and orthogonal frequency multiplexing found two different areas to be deployed in. In wired lines (xDSL), the channel is stationary over time, while the channel in WLAN and WiMax is not stationary, these two different channel characteristics forced the use of DMTF in wired media over OFDM, which found use in wireless channels (WLAN and WiMax).
DTMF is deployed as a number of modulated frequency carriers that can be spaced in any order, and each carrier is independently modulated (bit loading). This is contrary to WLAN, where OFDM dictates the use of uniform carrier spacing and a uniform bit loading for all carriers.
Another difference is also in the implementation, XDSL transmits baseband while WLAN/WiMax transmits passbad. With this, XDSL (DMTF) uses a technique that uses 2X FFT/IFFT to implement the modem, this is necessary to implement a real signal sent to the DAC.
In OFDM, this is not needed, since the base band (complex signal) is up-converted to a center frequency (i.e., 2.4123GHz).
There is also a difference in the channel estimation algorithm. The DMTF uses a one time before transmission channel estimation, while OFDM uses frame-by-frame channel estimation using two dimensional (time and frequency) preamble based technique.
Likewise, also, there is a difference in the method of channel equalization used. OFDM uses single tap complex channel compensation, while DMT uses zero-forced or other form of multi-tap equalizer.
There are also other differences that does not come to mind now, for instance, the fading or echo combating is done using cycle pre-fix as suppose to guard time interval,….etc.
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