You are conflating two different yet semantically related things.
"Work For Hire" and "Works For Hire" (sometimes referred to as "Works Made For Hire".)
Work For Hire refers to the actual work done by an employee/contractor that has been designated as falling upon the IP rules of Works Made For Hire.
Works Made For Hire is part of the the IP doctrine of copyright law.
If you are a contractor, and you do not have the money nor legal team to fight off an IP assignation case, you must carefully and clearly stipulate who owns what IP REGARDLESS OF WORKS MADE FOR HIRE. It IS ambiguous, and a contract lawyer will tell you - do not leave it up to interpretation outside of your contract..
I had a contract just two years ago that ran into an issue where the client (and their a**hole lawyer) were getting confused because I was going to provide them a solution that was built off of some code of mine that I owned all of the IP for.
I clearly delineated that they would own the solution, but that they were only receiving a license to use my previous inventions (and here's the part they choked on for a while) and any necessary extensions to my product that were necessary in order to provide them with a solution.
Their lawyer spent weeks arguing that they needed to own the changes I made to my existing product. That didn't happen...
So, as anybody who has dealt with an unfriendly lawyer would tell you - don't ASSume anything. Don't assume they won't be jerks, that they're not idiots, that the court isn't stupid, that jurors aren't stupid, et cetera ad nausem. Make it clear in your contract, as in 'clear to a 4 year old', who owns what, when, and for how long.