You are slightly confused...
It's like this:
- There is an application server, in your case WebSphere Liberty profile
- There is MobileFirst Server and Console, which are a set of .war and .jar files that are deployed to the application server
- There is your project's runtime, which is also a .war, also deployed to the application server
- There are the .wlapp and .adapter artifacts, which are deployed to the MobileFirst Server (or rather, its database, via MobileFirst Console)
This explains why you can deploy the .wlapp and .adapter remotely to MobileFirst Server, because it's a server and is supposed to be also accessible via the web (if setup properly).
But the .war file is an artifact that is deployed to the underlying application server (WebSphere Liberty) that runs everything, you cannot deploy it remotely - certainly not via MobileFirst Console.
If you want to attempt to remote deploy it via Ant, you can look at this question: Using Ant to deploy EAR to remote websphere application server (same concept).