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In this case, when you use the USB type-C port to connect a display, you are using the Display Port which is integrated to the same port.
Resolutions supported by the HDMI output and the Display Port are the same (4096 x 2160 @ 60 Hz); however, if you are using an adapter from USB type-C to HDMI, you are actually going from Display Port to HDMI).
In the specific case of the adapter that you mentioned, the max resolution supported is 3840 x 2160 @ 60 Hz, which means that by using this adapter, the max resolution supported by the Intel® NUC is being limited by that adapter.
Hope this information helps.
Please don't hesitate in replying to this post if you need further assistance.