Paradise and Heaven are two different things.The arabic word for heaven is sama' and the arabic word for paradise is jannah.First of all heaven is the skies or the seven heavens(skies) it above us and jannah is way beyond that is al-jannah which Allah has reserved for the munineen.Their is a sahih hadeeth which states the comparison one of the HEAVENS being placed in jannah( one of its levels) is like aring in a desert.So of course it is two different things Allah has mentioned both jannah and the heavens in Qur'an and both have different names so why would they if they were the same meaning.samawat=heavens and jannah=paradise.Even the ulamah have used in their books of hadeeth and other kinds when talking about jannah in English they say paradise.Allahu A'llam.