I agree that it's confusing. When I was in Egypt in 2020, the only museum was the one in Tahrir Square. The NMEC, which now houses the mummies, opened in late 2020 or 2021. Then, the Grand Egyptian Museum in Giza just opened -- or it may even still be in a soft opening. I imagine that there will be plenty of fanfare for the official grand opening.
They were moving a lot of things from the old museum to the the Grand Egyptian in 2020, and when I returned in 2021 it was almost empty except for the Tutankhamun artifacts, the tiny statue of Khufu, and the big statues. My understanding is that they plan to keep the old museum open, and I heard rumor that they are planning to display a lot of artifacts from Tanis, which they haven't had the space to display publicly. It will still be interesting, but it won't be the draw that it was just a few years ago.
The NMEC covers the entire history of Egypt from pre-dynastic times to the present. The mummies are the main draw at the NMEC. They had a huge parade through Cairo when they moved the mummies from the old museum. Honestly, having already seen the mummies while they were still at the downtown/old museum, I was a little underwhelmed by NMEC.
The Grand Egyptian Museum is a big deal. It looks out over the pyramids, and will display the entire Tutankhamun collection, which they didn't have space to display in its entirety at the old museum. They started construction in 2005 and they are just now finishing. That's the must-see museum now.
IMPORTANT ADDITION: You might want to find out where the Tutankhamun items are currently. I read fairly recently that the main hall is open at the Grand Egyptian, but the Tutankhamun exhibition is not. The Tutankhamun items will probably be the last things they move from the old museum. So, they might still be at the old museum.