Can anyone explain what the security implications are between these options and how they should be used?
In windows (10)
Run as different user Run as administrator
These two options have to do with account permissions which relates to file access, network access, and more depending on the policies within an environment.
By default in Windows 10, when you launch an application you launch it as a standard user. In some instances, the OS will determine that you need administrative credentials to launch the application and automatically escalate your privileges or fire off the UAC (User Account Control) popup to ask if you want to run an application. The system them tags your system utilization and the application permissions based off the user trying to run the application.
Now, some applications like the command prompt don't always require administrative credentials. In these instances, the command prompt will run as the standard user account even if the acting user resides within the administrative group. However, if the user needed to run an administrative task from the command prompt, they will need to search for the exe, right click, and select run as administrator. In this case, the same user account is associated with the application, but the application is granted system level access.
The remaining option, "Run As User" is really helpful in enterprise environments where a help desk agent may need to support a user. Instead of logging out of the user's session, an agent could enter credentials through a screen sharing session to launch standard user level access tools that are blocked by policy to the originally logged in user.
Lastly, there are instances in which "Run as administrator" is also run by a separate user from the logged in account. This will duplicate many of the effects of the Run As User but with administrative privileges for the application.