I'm assuming the stripes correspond with the existing cracks. It looks like your ceiling has a bit of "texture" to the surface and what they might have done is repair the cracks with some spackle or drywall mud, essentially making that section of the ceiling "flatter" than the rest. If you look carefully at a new house, you'll see the same kind of thing, where the joints are smoother than the rest of the drywall.

Another coat of paint would probably help to even out any color differences but the real fix is likely a skim coat over the entire ceiling to even things out. When painting a ceiling, make sure they use a flat paint, which will help hide any imperfections.

hopefully they did not use caulk, that will take paint differently.

Did they primer before paint? It is noticable, and I sure would not be happy. I dont understand why they would use caulking. It should have been taped and patched using sheetrock compound.

Those "stripes" look to me to be where you have had some movement/settling in the ceiling joists and the sheen from the new paint makes it more noticeable.

It's fine to use caulk for hairline cracks, as long as you fill the crack and have a wet rag or sponge handy to wipe all excess caulk away. You don't want any caulk in the field of the ceiling. It all needs to be in the crack. This is actually better because caulk flexes and patching compounds do not.

If it's not made right after they come in this second time, you may need to pay a little more for the same people to come back, or just get someone different altogether to do the work to your satisfaction. These kinds of things are good to remember for future work of the same sort, so that you (hopefully) can avoid having to give the next guy a second run at doing it to your expectations.

Painters don't seem very competent

The owner came and said the wide line I’m seeing is where his worker went over the line with a brush.

That's explains it. The part that was brushed then dried before the rest of the ceiling was rolled. The stripes ended up getting two coats, a heavy first coat of paint and then a thin rolled or sprayed coat, where as the rest of ceiling got only one coat of paint.

That's why you always need to keep a wet edge when you paint. Same thing has happened to me when I cut in the ceiling and the paint dried before I could get it rolled. More of a problem anymore because a lot of modern paint just dries faster. Add in ceiling work where the air is warmer and the paint dries even faster.