If you're confused, or comparing “Parasyte: The Grey” with the original, you should not. “Parasyte: The Grey”, as far as the hints they dropped in multiple episodes, is set in the same universe as the original Parasyte.

In other words, this is not your regular adaptation, it is a spin-off. It is called a “shared world”.

“Parasyte: The Grey” is set in Korea and tells the story of what happened when Parasytes landed in Korea. This is why there are a lot of differences, it is not an adaptation, it tells a parallel story. There are also similarities, and that can be easily explained as the world governments sharing information; as well as, humanity today thinks similarly, so we end up doing the same things even without direct contact.

Don't dismiss “Parasyte: The Grey” just because, otherwise, you're going to miss a greatly written live-action TV spin-off of the franchise. Again, based on the hints dropped in multiple episodes, this Korean spin-off exists in the same universe as the original material. It is, however, unclear if they directly based on the manga (the original), or the recent two-part Japanese movie adaptation.

If you're going to ask me, I think “Parasyte: The Grey” is closer to the two-part Japanese movie adaptation than the original manga and anime adaptation. But, that's not important. The important thing is, for the 3rd or 4th time, as per the hints, this series exists in the same universe as the Japanese story.

^_^