Daniel,
updating from v2.0 to v2.1 Elements (Windows), the update page does not list an Elements as a separate installer from the Pro version. Should it or do you use the Pro 2.1 installer? The way this reads (Dorico Pro 2.1 and Dorico Elements 2.1 available now - Dorico - Steinberg Forums) I looked for a link for the Elements installer assuming there were two installers for each platform. Maybe I read and understood it incorrectly?
Not knowing what to do, I used the Steinberg Assistant as you also suggest, so all is well. (I also have DP2.1 on Mac, but there was no confusion about this).
Elements and Pro are exactly the same program and exactly the same installer.
Each time you open Dorico it looks for an eLicense, which determines whether Dorico should run as Pro or Elements.
Thanks for the clarification PianoLeo 
Probably redundant information now, but just for completeness, I found a specific Elements v2.1 update page (for someone else) here: