Is this a correct explanation ?

You use "there" to introduce nouns. (There was a storm last night) Use "it was" -to introduces an adjective. You could say "It was stormy last night" because "stormy" is an adjective. Thank you !

I think your ruling is a bit simple. Both of these are fine:

There was a storm.
It was a storm.

"There was" introduces something that happened.
"It was" talks about something you've probably already mentioned.

The simplest things are always the hardest to explain. Good luck.

Thank you for the explanation, I get it!