All flames are fire, but all fires are not flame.

I will try to simplify as much as possible.

Generally, flame is controlled like the candle, lamp, LPG burners, which are fire used for either its heat or light.

Fire can be controlled too, and sometimes even used for heat or light or both, however, the exothermic reaction is on a larger scale and very difficult to control, like it has a mind of its own.