There are four different types of differentials: Open, limited slip, locker, and spool. Read this article to learn about these different types:
http://www.bc4x4.com/faqs/yj.cfm?cat=7&faqid=156
No matter what type of differential you have, you should never use 4wd on dry pavement. Because even though the left and right tires can spin at different speeds, the front and rear wheels are locked together and forced to spin at the same speed. When you try and make a turn, the front and rear wheels (as well as the left and right) need to be able to spin at different speeds (basically all four wheels need to be able spin at different speeds from each other), otherwise you'll get binding and can break stuff. On slippery surfaces, this doesn't really matter because the wheels can "spin out" and slip to make up the difference in speed. So no matter what, 4wd is for slippery surfaces only.
Most Bronco IIs have an open front differential. As Adsm said, limited slip was a rare option.
"Solid axle" refers to the type of suspension you have, not the type of differential.
This is a solid axle:
Notice how you have one solid beam, which has the wheels connected on both sides.
Bronco IIs have independent front suspension, shown here:
Notice you have two separate axle beams, one for the driver's side wheel and one for the passenger side. The beams pivot up and down when you go over bumps, and they can move INDEPENDENTLY of each other. Hence the term independent front suspension (IFS). Note: there are a few different types of IFS, this one in particular is called "twin traction beam." It's pretty much a Ford-only system, used on most Ford trucks from 1980-1997. Most other IFS trucks use an SLA front suspension (That's a Google term for you.) Hope this wasn't too detailed. Read it over slowly a few times if you have to, it'll sink in eventually.