Have done both, grits is more coarser and Polenta is finer BUT the mill grind is up to your taste as even commercially there isn’t really a standard.
Polenta is made with a finer grind my wife makes all the time and I use my Wondermill attachment for that. It is subjective though. Use the Wondermill for grinding rye chops, and Semolina also.
What mill are you using as this makes a difference. I have a Wondermill burr grinder which does a nice job of grinding coarser meals (without too much fine flour) and a Mockmill 100 which makes very fine flour if required. You can though open up the Mockmill to get a larger grind but it is a stone miller, I just found it makes more flour. No matter which you use you will get some fine flour with the grind and the finer the setting the more you will get. The more fine flour the more goo you will get that is why I use the burr grinder for meals etc. The only way I believe you will get only the coarser stuff without the flour is to crush the corn.
Sifting will get you the larger chunks, kind of a trial and error thing. I would think a very fine 50 mesh or smaller sifter would be a place to start as the holes are very small allowing just the fine flour to go through.
When Diane wants ground Nixtamal (lye treated corn) for Polenta, corn bread or corn tortillas, I start with a coarser grind and put it through a 2nd or 3rd time until the “boss” likes it. WORKS EVERY TIME! No goo!