Typically here a project manager works for the general contractor managing a project. Now your dealing with semantics.
*sigh*
First off, "you're".
Secondly, a project manager doesn't have to be licensed. Why do you think all those "home workover" and "home rebuild" and all those shows don't involve general contractors, but rather project managers?
General Contractors are like lawyers, doctors, pharmacist, etc. They are licensed by the state, have to take certification exams, have to carry very expensive insurance, etc.
Project managers don't. (There is presently a movement and pending legislation to change that, but at this point there is no requirement.)
So long as a project manager you hire certified people to do work requiring a certification (HVAC, Electrical, etc.) and have it inspected by the State/County building inspector and of course have the required permits for the work you're doing, then you don't need to hire a general contractor, you can hire a project manager.
The price difference is astronomical, and legally from the standpoint of building a house or deck, in most states you are not required to hire a general contractor, a project manager will do.
In the most layman of examples: I worked for Holder Engineering back in the late '90's. Holder was the GC of Gwinnett Arena, a 90 million dollar project.
Most general contractors wont touch a job that isn't worth multiple millions of dollars because they typically charge by percentage of the project.
So if you're building a 30,000 dollar deck, no GC is ever going to touch it. His insurance for the job would cost more than the 3 to 6 thousand dollar fee he would charge you.
Even on most homes, the fee isn't worth the risks.
Bob Villa even discourages hiring a GC for home construction because of the outrageous costs involved for what is in the grand scheme of things a small project. He has an entire section dedicated to how to do it all yourself and hire at most a project manager to oversee the project.