A “raid” is often planned in advance. “Storming” might be more an immediate action without as much planning. The police might investigate a drug cartel for a period of time and then carefully plan a “raid.” When there is a hostage that has been taken, they might “storm” the place.

A ‘raid’ is a little more organized and would be the more typical word to use here. A ‘raid’ can be a military maneuver. The soldiers raided the base. The crowd stormed the stage.

Apart from a potential minor semantic difference they mean the same thing :)