It's a very important distinction. I have worked WITH some great people in my career - and some of my supervisors have become lasting friends and taught me a lot. But unfortunately I have also had the experience of working FOR people in a very hierarchical setup, and I would never want to repeat that experience.
I ran my own business for a few years, and I made a big effort to treat my employees as co-workers rather than people working "for" me. I felt that if I respected them, they would enjoy their work, which was important in a public-facing business - I didn't want sulky people serving the customers. It worked more than 90% of the time. Sadly I had to sack one person whose behaviour was out of order, but the other employees were great.
Since I closed my business I have worked part-time for nice people who treated me with respect. I would never go back to being treated like an inferior.