"Paradise" is a specific person's perception of a perfect place. Some might find paradise a place of beauty, calm and peace. Other's might find it a loud, party or something. It's subjective. However, "Heaven" is more of a unified religious concept of a specific idea of paradise. Often people relate it to the place their "God" resides and cares for, and it's often related to the sky. For example when people say "look to the heavens" they mean look up at the sky. So yeah, you're exactly right!

Paradise and heaven interchangeably. But originally they referred to two completely different places. In the original languages of the Bible, heaven referred to the sky and everything above it, including the upper heavens where God was understood to dwell. Paradise, on the other hand, originally referred to an earthly garden, the Garden of Eden (which in the ancient Greek version of the Bible was translated “Paradise of Eden”). By New Testament times, “Garden of Eden” (Gan Eden, Paradise) came to be used in Judaism to refer to the place where the souls of the righteous went after death. This is still the understanding in Judaism today. And it’s still often described as a garden-like environment, as it also is in Islam. But this is a different place than the presence of God in heaven. This difference can also be seen in the Christian New Testament. When Jesus was on the cross, he said to one of the thieves that were being crucified with him, “Amen I say to you, today you will be with me in Paradise” (Luke 23:43). But three days later, after he arose from the dead, he said to Mary Magdalene, “I am not yet ascended to the Father” (John 20:17). And he didn’t ascend until forty days later (Acts 1:9). This shows that Paradise, where Jesus’ soul went immediately after death, was a different place than the presence of the Father God in heaven. Originally, Paradise was understood to be the “good” side of Hades (or Sheol), where all souls went after death. This was understood to be down in the underworld somewhere, an idea shared with many different ancient cultures, including ancient Rome and Greece, which also put the place of the dead in the underworld. That Paradise and Hades were very close to each other can be seen in Jesus’ parable about Lazarus and the Rich Man. The soul of the rich man, suffering in the bad part of Hades, calls out to Lazarus, who is on the other, good side (the bosom of Abraham, another common name for Paradise.