A solar flare, as defined by NASA, is an intense burst of radiation that results from the release of magnetic energy associated with the sunspots. A typical solar flare may last from few minutes to few hours and can be observed as bright areas on the Sun. Solar flares may also be accompanied by coronal mass ejection (significant release of plasma and magnetic field) and this ejection can extend up to thousands of miles from the Sun's surface. The solar flares have very broad spectrum emissions. A solar flare may present a radiation hazard to spacecraft and astronauts, and may adversely impact satellite communication.
A solar prominence, on the other hand, is a large and bright feature that extends from the Sun's surface. A prominence is anchored to the Sun's surface, unlike a flare, and is often characterized by a loop shape. A prominence is bound by the Sun's magnetic field and can last for months. A prominence can also extend up to thousands (or hundreds of thousands) of miles from the Sun's surface. These are typically harmless as compared to the solar flares.
Hope this helps.