In 2 Corinthians 12:2 talks about being caught up to the third heaven. What is the third heaven? What does it mean by being caught up to the third heaven?
The 'formal distinction' is a bit of a synthetic one. Remember why it's "God created the heaven [not 'heavens'] and the earth' --and then subdivided the firmament a bit later... you have multiple 'heavens' at different points.
The distinction as I understand it:
First heaven is the domain of the clouds, birds, air and so forth. Second heaven is the stars and planets Third heaven is where God is
Someone will improve the theology, but this is a framework to give you the sense of what he meant by the expression.