Let's say you replace a part in your car, it's still the same car, right? What happens if you replace half the parts in your car, is it half the same car? What if, over the years, you've replaced all the parts in your car... isn't that the same as just buying a new one?
I'M GONNA FIGURE THIS OUT YOU GUYS. HERE'S THE LONG ANALYSIS:
The ending is supposed to be a little ambiguous. With movies like these, the ambiguity is meant not to make you wonder about what happened at the end, but make you think about the overarching message. This film is heavy with philosophical concepts about thought, emotion, and life.
Descartes (a famous philosopher) said, "Cogito ergo sum" which means "I think, therefore I am." How does an organism survive if it cannot think? Instinct? What separates instinct from thought? Emotion? Rationality? These are the deep underlying questions that the movie explores and, purposely, doesn't answer.
There are two general conclusions you can draw from the endings, and I'll explore them more in detail below:
1) Primordial Ooze (we'll call it Po) "copied" the crew members. It returned to Earth posing as humans, presumably to conquer.
2) Po "healed" the crew members. They returned to Earth healthy, but traumatized.
So, evidence for the first conclusion...
We get a TON of info on Po from the scenes in med-bay. First, we learn that Po replicates any organic material it touches, as shown by the jarred body parts. It does this at an extremely fast rate, as shown in the journal. Whit's microscopic evidence proves how Po is a predator on a cellular level, fighting to kill until there is one clear winner. Survival of the fittest. Evolution on fast-forward.
It's also worth noting that, prior to this discovery, the crew considered Po to be a viral contagion; afterward, Whit realizes that it's actually a parasitic organism. He considers the possibility that the entire planet is one entire Po.

This is important because for the entire movie the crew thinks they are going to die. If Po is the predator, then they are the prey. Whit says that the organism is just doing what an organism does: it survives, regardless of what happens to anyone else. He says, "It's not capable of understanding."
Alright, let's move on.
Another point in favor of a species-dominating Po is the fact that EVERYONE DIES. Seriously. One guy gets an ax right in the chest, several people get shot in the head, another gets beaten, a unborn baby is unprofessionally aborted, and at least two people commit suicide. Not to mention all the people that were frozen and shattered to pieces. Over 1550 people. By our current scientific knowledge, humans aren't capable of rising from the dead.
So, if the crew is dead, Po must have replicated them in their entirety, right? This is why the ending scenes are so tense - Po has evolved from a simple I-Eat-Things mentality to having to deal with human thought and emotion. Po suddenly has to use its new collective brains to manipulate ACTUAL humans who have been playing the human game for a lot longer than it has. But remember, it adapts and evolves exceptionally fast.
But wait!
If Po is just replicating dead humans, why not replicate the 1550+ dead humans it has on hand? Granted, a lot of them are shattered to pieces from being frozen, but not a single one was reconcilable? While it definitely seems that an extremely low temperature is a weakness for Po, a lot of those bodies were thawed and still usable...
Shh. Po just learned how to use the human brain, remember? And it has smart brains, too. Surely it would have figured out that it's extremely suspicious to revive a ton of previously-confirmed dead people. That would lower its chances of infiltrating Earth and reproducing.
Okay, that's enough for Theory 1. Let's move to Theory 2.
The easiest thing to dissect is the whole replication thing. The main argument seems to be whether Po is replacing human cells with new ones or if it's healing the crew by replacing... human cells with... new ones? What? Surprise surprise - the actual healing process that our bodies perform on themselves could very well be the same that Po is doing to the crew. It's a semantic argument.
The next point is also pretty easy to break down: if the crew aren't actually themselves anymore, what's the point in discussing an excuse to return home with? The crew members, after being healed, gather and unanimously decide that depressurization caused them to have lapses in memory. They can't remember much, but they rescued Whit and stopped the hazardous materials from being teleported to Earth.
The scene clearly shows how emotional and traumatic the experience was for them - all they want to do is go home to their families.
Home. Family. It's a huge theme.
Whit has a pregnant wife. Huntington records an entry to his wife and child that he knows won't reach Earth until they're long dead. Claire has an unborn child with Morgan. Menzies has a daughter who didn't want him to leave.
Daddy loves you all the way to the Milky way. The long way, not the short way.
So here is where I tell you that I've already made my decision. I whole-heartedly support Theory 2, and believe that the crew returned to Earth 100% human. Here's why, just bear with me.
Po, simply put, is really freaking big. It's so big, it was mistaken for a planet. If Po has an exceptionally high rate of adaptation and accelerated evolution, how has it survived so long without developing higher intelligence? The answer is simple: there was no higher intelligence to replicate. Until now. In nature, higher intelligence doesn't necessarily equal better survival. But it does when you are trying to compete with intelligent organisms. When Po began to replicate cells (brain cells, as seen in the med-bay), it quickly adapted to its newfound awareness. It was suddenly smarter and craftier... the emotions came later.
"You couldn't get past your own selfish, ignorant need to dominate. If you had time to grow, time to evolve, things could have been different... we could have worked together."
Home. Family.
Why did Po save Whit's family photo at the end of the movie? It couldn't have served any practical purpose. It was a memento, a reminder of the experience of his emotion, of family and a sense of purpose.
Why did Po decide to reveal itself as multiple human-like shapes? Family. Po made a family for itself.
Why did Po heal the crew? So they could go home. And Po didn't have to travel to Earth because it was already home.
Let's bring this full circle.
Whit Carmichael: I was never meant to be here. All I was trying to do was make a better life for my family. And you took that away from me. You took that away from all of us. And now look where it's got us. Whatever you tried to do here. You failed.
Claire Grenich: I'm so sorry Whit. We were supposed to get you home.
Whit Carmichael: It's not capable of understanding, not yet anyway.
Claire Grenich: A child needs support on all levels.
Whit Carmichael: I promised my wife I'd be home for dinner.
Rex Mannings: This moment right now, Whit, is life. And life is nothing, without choice.