Duplicate of photos? Given latest versions of MacOS and iOS and one iMac and one iPhone both on the same iCloud account.

I take a picture with the iPhone. It shows up, via photo stream on the iMac. So far so good.

Now I attach the iPhone to the iMac and do a sync. Does the photo now "live natively" on the iMac or still just through photo stream? I think it's not native yet.

Now I use Photos app on iMac and import the photos from the iPhone. Now the photo lives natively on the iMac but it looks like I have a duplicate because the stream copy of it is also there.

That can't be right can it?
I would not sync, so no this isn’t right IMO. Use iCloud if you want to sync photos between a Mac and an iPhone is my advice.