xhuke has provided a good description but many instrument manufacturers tend to use the terms to define where the transducer data is processed to provide the measurement in the appropriate units. For example, the term transmitter can mean a device e.g a density meter, which transmits an output in the required units e.g. a 4-20mA signal proportional to density in kg/m3.
A transducer is then an instrument which transmits raw sensor data for remote processing. In the case of a vibrational density transducer this is a frequency. Frequency is proportional to density but must be corrected for a number of effects including temperature, velocity of sound, viscosity, pressure etc. This is then done in remote electronics.
transducer by a technical dictionary: Any device or element which converts an input signal into an output signal of a different form; examples include the microphone, phonograph pickup, loudspeaker, barometer, photoelectric cell, automobile horn, doorbell, and underwater sound transducer.
transmitter: ICman is right, sometimes words are used indistinctly, as in telephony, the carbon microphone that converts sound-waves into audio-frequency signals is called a transmitter, and by the above description it would be a transducer. A radio transmitter would be defined as the equipment used for generating and amplifying a radio-frequency carrier signal, modulating the carrier signal with intelligence, and feeding the modulated carrier to an antenna for radiation into space as electromagnetic waves.
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