What is the difference between smoke damper and firesmoke damper?

Assuming your question relates to life safety in building construction, and not to parts of a wood burning device- Smoke dampers are intended to limit the movement of smoke within a building, or section of a building. They are not intended to inhibit FLAME spread. A fire damper will inhibit smoke movement, but is also insulated to stop fire. A simple smoke damper might be light weight sheet metal- but that is not enough to stop very high temprature. A fire damper is heavier, may be insulated, built of fire resistive material, etc.