Hi pcora,
I am not with Laminar Research; just a flight simmer.
From your initial query I assume you downloaded the digital demo version from the Laminar Research (LR) site.The steam version is a hybrid of the official Laminar Research (LR) digital download version and as Tyler has stated they don't mix and are not the same product You will have to totally delete the LR version. Any updates released by LR are delayed through the steam version.
If you had downloaded the demo version from LR why did you purchase the Steam version as you already had the official version on your machine? All you needed to do was pay for the official LR version and then apply the password/download key to unlock the demo version. Updates from LR can be immediately applied at the time of release and if you are so inclined you can update with the beta versions as well.
By the way I am not a steam user and don't support the product.
Glenn