Hi Jeff,
They are not storms in the sense of being rain storms or thunderstorms, so you could say that "solar storm" is a metaphore.
Conditions in space can change sudenly and be disturbed for a while, so we are comparing that to storms in the atmosphere which can lead to sudden changes and disturbances for a while. We use a number of comparisons like that, for instance "solar wind" , "space weather", "geomagnetic substorm"
"solar storm" is not really a technical term (although those other terms all are). We usually use "Solar storm" when we are telling the public about coronal mass ejections (CMEs). These are disturbances in the solar wind - so we are making the comparison to Earth atmosphere storms. They are very different in most of their details, though.
Terry