One thing is for sure, you learn as you go. Above, you can see my original sort of Other Uniform buttons. After doing some research, I do not think I classified all of the buttons correctly. Instead of reclassifying, I thought I would talk about the challenges of figuring out exactly what you have.
First, let me show you what I did identify that I think was spot on. Below, see the Military and Uniform buttons that I was positively able to identify. I am always amazed how some of these buttons find their way into jars of buttons. Military buttons are always well designed. Most are very well made and have worn well. That is a lot of "wells". Identifying them might take a little bit of work. I found fairly generic military buttons that were easy to identify. For example, buttons with the British Royal Crest are most certainly English. I had a good guess that the crown with the anchor was also British. I was able to identify the three crowns as Swedish because of my ancestry. From experience, I was able to identify a buttons with a P on it as a Police button, just as FD stands for Fire Department. That is where easy stops.
A buttons with a crown does not necessarily mean Britain. French, German, Swedish and Spanish military buttons can have crowns. Buttons with Eagles and stars are usually US but the US was not the only country to use Eagles on Military buttons. A two headed eagle could be German. Several countries have castles on buttons. If you are lucky, the button may identify the unit. If not, you might have to start researching. There are not only military buttons but State buttons, airline buttons, ship buttons and school buttons. There are a large array of Golf Club buttons that are highly collectible so look for a golf club. Some golf club buttons are the genuine thing and others are simply suit coat buttons with a golf club. The Big Book of Buttons is a great place to start. Consider requesting the book through inter-library loan. There are also collector web sites that might help identify a particular button.
I originally had classified certain buttons as uniform in my original sort. Now, after doing some research, I am not so sure. Check out the pictures below and how my original assessment changed.
I should also add that one of the best sources of information on buttons are button collectors. I always welcome their knowledge and expertise. I never mind having them correct me if I am wrong. That is how we all learn.