Do dishwashing detergent and stain remover powder/stick have the similar ability to remove collar rings?
Detergents seem to consist of both polar and non-polar compounds. Probably because they need the non-polar part of the mixture to dissolve the grease, and the polar compound part of the mixture to get washed off with the water so there is not much left over on your shirt. The ideal solution would probably depend on just how bad the stain is (how much grease needs to be dissolved). If your home solutions did not work the first time, try to look for signs if it did anything at all, and it might not be something that will remove all the grease the first go around.

I have no experience using detergents or removing stains, but I am going off a lot of speculation here as to how the process might work.

"Like dissolves like"

According to this article if there are lots of Mg, Ca, or Iron ions in your water (likely) then it could reduce the effectiveness of soaps. A good question to ask yourself is whether or not your water contains many ions such as these.