The one on the left is a regular ("Milton" style) fitting for your typical air tool, DA, impact, etc. The one on the right is a high flow fitting. Those are great for HVLP spray guns and anything else that takes ungodly volume. The high flow ones work great for anything, but using the smaller one can cause problems with high CFM tools. Look at the I.D. and you'll see the high flow one is larger.
Hope this helps Bill.
Learn something new everyday. I always just went with what the shop was set up for.