Chuck,
Actually there is a similar concept which may work for you... the ArcGIS Runtime cannot be licensed directly with "ArcGIS Advanced licenses" as was the case for ArcGIS Engine. Instead, licensing of ArcGIS Runtime applications is achieved via one of two routes:
1. An organizational account on ArcGIS Online or Portal for ArcGIS (on premises or private cloud)
2. A license code from a purchased pack of licenses.
The good news is that if your ArcGIS for Desktop licenses (you mentioned "ArcGIS Advanced" above) are in maintenance then you may be able to claim a free organizational account, which would mean you could effectively license your Runtime apps because you have the desktop license, i.e. similar concept as for Engine but the technology has moved on. These free subs are renewed annually when you renew your maintenance. To find out if you qualify, you should contact your Esri account manager / distributor. If you license your apps this way, your users will need to log into ArcGIS Online every 30 days in order to renew the license.
If your app needs to be disconnected, or the 'named user' licensing model doesn't work for you, then you can purchase packs of licenses. In this scenario you get one license code/string to embed in your app and you reuse that code in each deployment of that app. If you exceed the initial number purchased, you just buy more and keep deploying.
For more info see License your app—ArcGIS Runtime SDK for .NET | ArcGIS for Developers
Cheers
Mike
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