If I understand your question:
The DB ADK is for single connection, standalone applications. For instance, a budget application that manages the expenses of a single user installed on a single computer. Like Apple's now defunct Bento Database app. No network connectivity.
VServer is a standalone database/report server that is accessed in a client/server scenario. Such as the budget app above, yet it connects to a separate VServer via the network that handles many connections at once. Like an office full of people running your budget app connected to the server on a local or remote network where they can all share the data. There is no separate app to manage the VServer - clients just connect to it. You use Valentina's VStudio to do manage the VServer.
Embedded VServer is for when you write your own application that handles the business logic and/or back end code for your budget app server branded under your company name. For example, you write a app that allows you to manage all the aspects of an Embedded VServer externally and all the additional functionality you need. Like VStudio when connected to a VServer - but your app does this instead because you don't distribute VStudio to your clients. "Scott & Company Budget Server" is installed on a client's server. This app uses the Embedded VServer as its database. Your Budget Server app handles all the functions and services of your client budget applications when connected to it via the network.
Basically, it boils down to two things:
1)
How will your database be accessed? By one single person on his/her machine only? Use the DB ADK. Or by many people through a network. Use VServer or Embedded VServer.
2)
Licensing. If you purchased a VServer license, you can install it on a machine you own for your own use. I have an unlimited VServer license that I use for my office. It is installed on a server I own that I use in my office for all my employees to use for the in-house apps we write and reports we generate. I also have a VDN Developer license (Embedded Server) for the apps we create that use Valentina as a database server branded under my company that we distribute/sell to people royalty free (shameless plug there...).
Hopefully this makes sense. Lynn can probably explain the licensing details a little better than I can.