According to the Wikipedia page regarding the ultimate fate of the universe, heat death is a different scenario than the big freeze.
It states that in the big freeze, temperature will asymptotically approach absolute zero. However, the following section about heat death states that heat death may only occur if temperature reaches an eventual temperature minimum.
If temperature never truly reaches absolute zero (the temperature minimum), can heat death even occur in the first place?
The Wikipedia article is somewhat confused on this point (at least one of the references does not support the sentence it is supposed to support).
The classic concept of the heat death of the universe was that eventually it will run out of free energy and there will hence be no possibility of any work. A more modern view of heat death is an approach to maximum entropy where the system will be in equilibrium. This does not rule out random fluctuations bringing it away from equilibrium, but they are so rare it does not matter.
Note that it is entirely possible to have a heat death at any temperature.
The big freeze would happen if expansion of the universe led to temperatures decreasing towards absolute zero. However, if there is accelerating expansion this generates a constant finite temperature horizon radiation, about $10^{-29}$ K. This means that the big freeze will never happen.
Had there not been horizon radiation it would in principle have been possible to avoid heat death by storing some background heat in a perfectly reflective box, waiting until the universe become colder, and use it to perform work. This can be repeated indefinitely. (Not really: the timescales quickly become long enough that random fluctuations destroy your device, but that it a separate issue).
Due to the universe not only expanding but gaining speed, it's pretty well accepted (for now at least) that galaxies will be sitting alone, or maybe with other gravitationally bound neighbor galaxies, as the rest of the universe goes dark all around. Eventually our home galaxy would burn out it's last star. Thats the big freeze, and not happening for a while... The end stages at least. Its seems like heat death is a variation to the big freeze, except expansion somehow stops for heat death? and im not sure what the universal temperature is thought to plato at, but after all thermodynamic process' end, the universe' energy will be lost to the void and entropy will reach its maximum as universal equilibrium is reached (uniform temperature and lack of activity) but tthe time it would take for the last black hole to evaporate is so long it's hard to comprehend, 10^100 or a googol years, if im not mistaken. heat death and the big freeze seem like different ways of explaining the same event, the former being on a longer time scale, but both seeming headed for the same fate. and wiki and google agree most of the time, but a few articles off a google search said the opposite. I think maybe you read some info from contradicting sources is all, if there is a difference in these two, its that expansion stops for heat death, allowing a marginally warmer universe than one with infinite expansion. there is no reason to think thats going to happen with our current understanding of dark energy.
