"The storm is coming."
What is the difference between a storm and a tempest?
You can treat these two words as synonyms. There may be some subtle cases where one is appropriate but the other may sound irregular, but generally, when you learn a foreign language you usually don't get such subtle differences.
If you're talking about a real storm - like when there are strong wind and heavy rain - you can use either. If your storm is metaphorical, like strong emotions within your mind, then סערה is appropriate, but סופה is not. If you're brainstorming you'll use a verb derived from סערה, we call it "סיעור מוחות", not anything derived from סופה.
So as a summary, use סופה only for weather, and only when the winds are strong. Otherwise, use סערה. In fact, you can always just use סערה.
Seems that סערה is way more common, and that there is a meteorological difference between the two.