The difference is you can fire clients. It's hard to fire bosses. Plus you should be seeking multiple revenue streams.
The stability of a "job" comes from a regular paycheck and not having to do the work in addition to sales. Roughly 50% of the time working as a independent developer should be spent (IMO) working to add new clients and/or expand your revenue stream. If it gets to be too much work, you've now got a consulting company with people working under you (and the nightmare expands).
I don't consult anymore, I have a SaaS company now. But when I was consulting I got to the point where I had a small, loyal group of clients who always needed work every month and always paid their bills without complaint. I would pick up new clients very selectively. I also employed a few developers and had payroll to meet.
Of course I could fire any of my clients at any time, but it would have only been harmful to my business. They were great clients and I wanted nothing but to keep them happy. Thus the "illusion" of freedom as I mentioned.
I was in very much your situation a year ago or so.
An "illusion of freedom" would imply that you think you're free, but in reality you are shackled. However, you not firing your clients was a choice. And I guess it wouldn't have been so bad for your business as much as it would have forced you to look for new clients with whom to create new relationships from the beginning.
To turn this into a potentially idiotic analogy, let's put it in terms of a romantic relationship: If not being married gives you the freedom to easily move onto a different relationship, it doesn't become an "illusion" just because you don't break up. You're still free to do it, you just need to justify it to yourself.
The problem I've run into with terminating clients is that most of them feel that if the project was not 100% complete for what they paid, then nothing was done, so you end up in a huge mess of keeping the money they paid you already but suddenly feel entitled to.
Try breaking up projects into several milestones, where each milestone has a concrete deliverable that would be useful if they took it to another contractor.
That way, they have valuable deliverables that they can take to another developer if you end up firing the client.
This is why you have a work product that's got weekly deliverables you have them sign off on. Also you have them pay as frequently as you can get. Typically with contracts I have it done weekly. Tried monthly but that can get annoying.
The stability of a "job" comes from a regular paycheck and not having to do the work in addition to sales. Roughly 50% of the time working as a independent developer should be spent (IMO) working to add new clients and/or expand your revenue stream. If it gets to be too much work, you've now got a consulting company with people working under you (and the nightmare expands).