It seems to me in the Bible , paradise and heaven are two different things . Heaven or the heavens is meant to be the sky, where the stars are etc " And a great sign appeared in heaven" Whereas paradise is where the good go when they die . " Today you will be with me in paradise" I don't get why we don't use the terms in the catechism, it makes things complicated.
Heaven can mean like in astronomy ("stars in the Heavens") or Paradise. That's my understanding anyway.
The sky, space and everything within creation above us is the heavens. Heaven with a capital H is outside of creation with God. That can be referred to as Paradise as well. Remember the word paradise could also be used for labeling things within creation. The Garden of Eden was called paradise as well. Yes it can be a bit confusing. Could be in the simplicity of English language versus the true source languages of the early bible; Hebrew, Greek and Latin. I am not an expert in those languages though to know if there is deeper meaning in the definitions used for Heaven and heaven or Paradise and paradise.
