There have been many changes to Terminal Services since the 2003 days, the least of which is the name change to Remote Desktop Services. Here are some of the useful resources for getting acquainted with the latest capabilities and how to migrate to the latest versions.
I've included this link because it covers some of the RDS licensing requirements when the Essentials Experience is enabled on Windows Server 2012 R2 Standard and Datacenter editions, related to the use of the Remote Desktop Gateway role inside of the Remote Web Access feature.
Migrating a Windows Server 2003 Terminal Server License
This guide describes how to migrate the Remote Desktop Services role by providing preparation, migration and verification steps.
Migrate Remote Desktop Services to Windows Server 2012 R2
This guide describes how to migrate the Remote Desktop Services role by providing preparation, migration and verification steps.
Remote Desktop Services migration and upgrade guidelines for Windows Server 2012 R2
To help with the migration of existing deployments this outlines the supported operating system (OS) upgrade paths to Windows Server 2012 R2 for all RDS roles, along with recommendations on how to upgrade in place an existing VDI deployment, with as little disruption as possible.
Remote Desktop Licensing website
This secure site is designed to help you manage your license server for Windows Server 2012, Windows Server 2008 R2 , Windows Server 2008, Windows Server 2003, or Windows 2000 Server, and for you to obtain Remote Desktop Services client access licenses (RDS CALs).
Migrate client access licenses
To manage your license server, go to the Terminal Services Licensing website, where you can activate a license server, install CAL tokens, reactivate a license server, and manage CALs. If you experience issues, use the Telephone method described in the following steps.
Remote Desktop Services – Upgrade guidelines for Windows Server 2012 R2
This document outlines the supported upgrades and interoperability for RDS features, as per Windows Client and Server guidelines.