A sensor senses something, a transducer provides a signal from a sensor that can be interpreted by something else that needs a format other than what the sensor works with.
So if you have a simple limit switch as a sensor, it probably does not need anything else to make its information useful. You just wire the contacts of the limit switch into the control system.
But if you want to measure current going through a 1000A busbar, you don't want 1000A going through your meter. So you can get a current "transformer", which is a rudimentary form of "transducer" to bring the current down to 0-5A. But typically if all you are doing is changing a type of value from one level to another level, but it remains the same TYPE of value, then we just call them transformers.
If however you then want to put that current value into a digital system, then you need something else that changes that 0-1000A current value into a signal that can be processed in the digital device, such as 4-20mA or 0-10VDC. The device that completely changes that current value into a totally different type of signal is what we typically mean by a "transducer". In some cases transducers need to have transformers as well, like in this case, because you cannot deal with extreme values and maintain accuracy. So in the above example if you want to look at 1000A, you use a CT to transform it down to 5A, then use a transducer to convert (transduce) that to 0-10VDC to go into a digital meter.
A transducer will also be necessary to change a physical property to a working signal as well, i.e. pressure to 0-10VDC, or level to 4-20mA etc. etc.
__________________
** All I every really wanted to be, was... A LUMBERJACK!.**