No, the Big Rip =/= the Big Freeze.
If dark energy's current strength increased, the universe would expand at an exponentially faster rate. In roughly 20-30 billion years objects, even if bound by gravity, would fly away from eachother. First galaxy clusters, then galaxies, stars and so on. Ultimately space would be a soup of neutrinos and other subatomic particles. Everything would disintegrate and time would stop (because the fabric of space/time would RIP), marking the end of everything. This scenario is the second most unlikely, after the Big Crunch.
The Big Freeze however is and ending where dark energy's current strength remains the same. So only objects NOT bound by gravity would fly away from one another. So stars away from one another, and planets away from stars, and their orbiting bodies. But the bodies themselves and their atoms will stay intact (so there would be no heat because the nearest star would be flying away at speeds faster than the speed of light, really cold, big FREEZE). This is the most likely scenario for the end of everything
I read this book called The Universe every night ahah. I am getting this shit straight from pages 54 and 55