How to explain the discrepancies between the end of Prometheus and the beginning of Alien?

Prometheus and Alien deliberately share a lot of themes, as well as the same universe, but they are not directly prequel and sequel (spoilers follow...)

1. The Space Jockey in Alien is old enough to be fossilised. Possibly by the same events that wiped out the Engineers in Prometheus (2000 years ago according to Shaw's carbon dating) but too close to Alien's dates to be the same one.

2. The planets have different names: LV-223 in Prometheus and LV-426 in Alien.

3. The planets have different atmospheres - LV-426 is "primordial" while LV-223 is "almost breathable" except for the too high CO2, which is not the case in the pyramids.

4. There are no alien structures on LV-426.

5. The ship in Prometheus is carrying black goo vases, but no eggs. The one in Alien lots of identical eggs, but no black goo.

So what is the same?

1. The Space Jockey in Alien is a giant 'human' in a suit.

2. The black goo is the source of both the alien in Alien and the various things in Prometheus. The DNA of its victim species has some effect on the result, and the final result in Prometheus is approaching the alien from Alien.

3. The eggs being carried by the crashed ship in Alien are probably the result of the black goo on something other than human, maybe something that layed eggs instead of giving birth.

4. I think that the ship in Alien is another attempt to wage biological warfare by the space jockeys/engineers. Either the eggs are before or after the black goo - both obviously went wrong so it's hard to guess which attempt came first.

5. The space jockeys/engineers share humanity's propensity for building really stupid ways to kill each other, as well as our DNA.

Ridley Scott has said that he envisions Prometheus as a trilogy, so maybe this gets tied up somehow.

The moon visited by the Prometheus, called LV-223, is not the same planet visited by the Nostromo in Alien, which is called LV-426. I believe that the latter was not named on screen until the second film, Aliens. So they are two different Engineer ships and two different dead Engineers.

Similarly, the distress call/warning intercepted by the Nostromo was in an alien language and needed to be decrypted, so it was not the warning in English sent by the humans in Prometheus.

Ridley Scott has stated clearly before this movie was released that it is not a prequel to the Alien film. It takes place almost a hundred years before LV-426 is found.

With that said, Ridley Scott has talked about making a trilogy of the Prometheus films. We can assume that the strange looking xenomorph shown at the end of Prometheus is an early ancestor to the xenomorph shown in Alien.

Is this the mother to all aliens or just an example of a xenomorph hatched from an Engineer?

Updated Sept - 2016

I read an interesting interview with Ridley Scott in which he explains that we never see the original xenomorph that laid the eggs in the dialect ship. Not in the original Alien (1979) film or the follow up Aliens (1986) film. In both of those films the xenomorph seen was birthed from human DNA, and the xenomorph shown in Prometheus was a human/Engineer hybrid.

Ridley has also stated he will not be returning to the planet visited in Prometheus. So the genealogy of the xenomorph born on that planet will remain a mystery. He's also stated that in the coming films he wants to explore new design ideas for the xenomorph.

As for the size of the Engineer in Prometheus compared to Alien (1979). Some people on the internet have verified that at the end of Prometheus when the Engineer takes the cockpit chair. He is the same size relative to a human as in Alien (1979). The issue is that the Engineer's in Prometheus are not wearing the same spacesuit when they are not in the cockpit chair.

The answer seems much more obvious than comparing moons and what not.

At the end, David informs Elizabeth Shaw that: 'There are many more ships'. In Alien, it's just another ship with another Engineer.