What is the difference between transistor and transformer?

It would be much less time consuming to name the things that transformers and transistors have in common than to try to name all their differences. In fact you named about the only thing the two have in common in your question. Here is a few of the many differences in the two.

Transistors can amplify complex ac waveforms without distortion much better than transformers can especially at higher frequencies. Transformers are unable to amplify (step up) an ac input Voltage without reducing (stepping down) it`s current capability. Transistors can amplify both current and Voltage at the same time.

Transistors almost always require a dc Voltage to operate whereas a transformer`s coil windings never requires a dc Voltage to operate. Sometimes a dc Voltage might be present in a transformer winding but the dc is not required for the operation of the transformer. A transistor actually modulates a fixed dc source Voltage in response to an ac input Voltage to obtain Voltage amplification whereas a transformer has more winding added to it`s secondary winding to obtain Voltage amplification.

A transformer`s input current is proportional to it`s load current whereas a transistor`s input current is normally almost independent of it`s load current. There are many, many other differences.