Consider it this way as an example:
I am Firewalker, a Nephilim. By no means a weaponry expert, I do know my way around small arms enough that It would be plausible to consider myself having two ranks in small arms. However, I am quite familiar with pistols and how to use them effectively in combat giving me a rank of four in pistols. That would mean I’m more experienced in the skill of using pistols while I’m only mildly educated in the field of small arms.
The fields are more for "Jack of All Trades" while the skills are more focussed "Expert" aspects of each field.
Like having general knowledge of famous painters and art types doesn’t make you an artist. By the same token, being skilled with a paintbrush doesn’t mean you know a lot about art.
This is just how I interpreted the rules… I hope it’s right, and if it is, I hope it clarified things a bit.