How SQL Server distributes queries between Database Engine and FTS Engine
You might find the diagrams and explanation found in the SQL Server 2008 R2 documentation useful. (Nothing has fundamentally changed recently on Full Text processing.)  

https://technet.microsoft.com/en-us/library/ms142541(v=sql.105).aspx

Quoting from that explanation: "The query processor compiles and executes SQL queries. If a SQL query includes a full-text search query, the query is sent to the Full-Text Engine, both during compilation and during execution. The query result is matched against the full-text index."

So you might view the Full Text search as a 'function' that returns its portion of the query from the Full Text Engine, then joins with any operators from the Database Engine that may also be part of the overall SQL Server query.