It's difficult to know where to start, because I'm a bit confused.. but you seem to be too, so if I was that confused with my own set up, maybe I'd start with some testing.
Suppose you draw 10 boxes in illustrator, and fill with shades of gray... 10% thru 100%
At least on the first test leave the CMY values at zero
Forget about cutting as that's not the issue, and just print a few tests.
First, print the vector file. You said that works good, right?
Then in illustrator... (No dragging) go to file menu, and EXPORT the file to a rastor image... and here you can choose file type, so I would choose a .tif format (which is how I've printed 99% of my work the last 10 years) AND here is where you can choose to export as RGB, even if the vector file was built using CMYK (which again is how I happen to work)
For your testing, if you export "full size" vector data, to become an RGB rastor file ready for printing, and you also create a CMYK rastor export as well, you can see how these compare with your vector file. You can also text 150 dpi vs. 300 dpi. For simple gray boxes, I don't expect you would see difference between 150 & 300, but I'd take this whole testing idea further into other types of tests because you can start to isolate issues this way, as well as learning about the tools of your trade and the workflow & production methods available to choose from.
Talking about dpi or ppi isn't sufficient without talking about file size and output size. I think you mentioned wraps. I haven't done a lot of wraps, but over half the ones I've printed are box trucks, and I might have 40 sq ft in each panel... if I started with vector data on that, I probably export it at 80-90 dpi and I get a file size of around 100 mb (which is about as large a file as I ever wish to wait around for ripping)
When I'm designing this box truck though, im probably working in illustrator at 1 tenth scale, so before I export, I need to enlarge to "full scale" (the size the print needs to be) ...if I forget to do that, my 90dpi file might only be 10mb and if I enlarge it to full size at the printing stage, it's going to look like crap... even if it was just a test of a black box, it will be blurry on the edges, and possibly in the center the color will suffer...
Anyway, to even explain issues, every step needs to be clear... Image size, resolution, & color space... in what program.... then performing what function ( exporting, dragging, opening in another program) and once you are in another step, like modifying the file for printing in another program... state how you get the file there, what its size, resolution and color space are... and then what size resolution and color space you are printing it at...
Without telling everyone EXACTLY what you are doing AT EVERY STEP OF THE WAY... you're just wasting your time and ours!
