Well you might have thousands of definations regards the topic even i have them none of them ever stayed.
This is a question & every engineer should know the answer.

Sensor reacts to a physical,chemical & biological condition.It senses.It can be considered as a detector.

The conversion of Energy from one form to another is called as transduction and a transducer serves this purpose.

A Sensor can sense in any form i.e due to some mechanical change ,it can react in electrical form.Thus their is a conversion similar to a transducer.
It means a Sensor can be a Transducer.
Eg ..Thermocouple
A Transducer is more than a sensor.It consists of a sensor or actuator along with a signal conditioning circuit.
A signal conditioning is a circuit which conditions the signal so it is strong enough for further processing.
So one way to define is that output from a sensor may or may not be meaningful.The transducer output is always meaningful.
The output of a motor is always meaningful that of a load speaker always meaningful.They are transducers.

Every Transducer is a sensor but every sensor need not be aTransducer.