I have a feeling the “Debian desktop environment” is just a set of basic desktop utilities and xorg GUI manager. It’s not an actual desktop itself. To that end, it might have been less confusing if they had called it “Debian desktop utilities”.
I think the confusion originally arose because, up to and including Wheezy, if no actual desktop was selected in addition to the “Debian desktop environment”, Gnome 3 was installed by default. But, this has since been remedied in Jessie onwards. Now, if you do not select an actual desktop in addition to “Debian desktop environment”, you will not have any of them installed by default.
The important point to note, here, is that if the “Debian desktop environment” is de-selected and a given desktop (such as, say, Mate) is selected, then following the installation, the selected desktop will not be immediately accessible due to a lack of basic utilities, such as xorg. This is because such desktops do not come with these utilities included.
So, to have full and immediate access to one’s chosen desktop following initial installation, one should allow the installation of the “Debian desktop environment” at the same time as the chosen desktop. Though, of course, one could alternatively choose to manually install said utilities including xorg at the CLI following initial installation
Or, finally, one could just install the base system and do everything manually at the CLI following initial installation.
It’s a very flexible installation system.
e.g.
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base system
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base system + Debian desktop environment
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base system + Debian desktop environment + chosen desktop
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base system + chosen desktop
Number 3 is what most people, most of the time, should choose.
Unless I have got it all completely wrong - in which case, people should ignore everything I have just written…