Hi Alex,
I suppose you can call a solar storm any fierce explosions from the Sun, including flares, prominences and coronal mass ejections (CMEs).
An intersting question that has puzzled scientists for quite a long time is the role of these different explosions in causing magnetic storms at
the Earth. Now it is believed that CMEs, that are huge explosions of mass and magnetic field reach the Earth's orbit and lead to the biggest magnetic
storms. When a CME occurs one often observes also a flare and an erupting prominence. However, their relationship is still unlcear.
Cold and dense material that prominences are made of are sometimes observed within CMEs at the Earth orbit. Also corograph images that beutifully show
the CMEs near the Sun often show a bright blob of material within a CME that is thought to represent the prominence material.