Trail running is almost the same as running on pavement with two key differences. First, the ground is uneven, so your feet need to be stronger and more flexible. Oddly enough, the same is true for running on grass. Second, you may have to lift your feet over obstacles. For me that meant failing, getting a big bloody flapper on my toe, and then doing it again. The second time really made my eyes water, but somewhere in my brain a switch flipped and I got a lot better at clearing things instantly. If you're running on clean pavement, you can add the need for adjusting your foot placement on trails, but much of the pavement I run on has glass and gravel and questionable fluids and trash scattered on it and zoning out on foot placement is a bad idea.
Walking barefoot is much that same as walking shod except that you don't bang your heels down as hard. Heels still touch first on easy ground, but more on the bottom of the heel rather than the back corner. On rough or sharp ground, you'll instinctively switch to a forefoot-first placement. On very smooth or wet surfaces, you'll find that bare skin has less traction than rubber, so if falling would result in death or serious injury, it's not worth pushing forward just on principle ...
As to all the different shoes for different activities, I think it's more about selling many pairs of shoes than it is about providing a tailored experience. In a decent pair of minimal shoes, my favorite is the Vapor Glove, you should run and walk and hike exactly the same way you do barefoot. Note that I say should. The extra protection allows you to cheat. Don't do that.
