What's the difference between microfiber and nylon, specifically in terms of apparel?

Microfiber means the fibers of the cloth are very small (measure less than 1 denier). Nylon is what those fibers are made of.

As for a base layer for your hiking trip I would recommend buying merino wool base layers as it much more comfortable to wear, will keep you warm even when wet and will stay smelling better for longer. Man made fibers will stink before the end of the first mile.

As described above, micro is just what it says, teeny tiny fibers. They are much softer than the old-fashioned kind, and repel dirt and water. However, that means by their very nature, they do not absorb liquids such as sweat. Do not use against your skin when hiking or exercising.

They are extremely good for outerwear, due to being very light weight, and their repellent nature. They also do not crease as easily cotton and other fabrics will, yet they retain any creases that are heat sealed into them.

For hiking choices, the shell of sleeping bags, and backpacks and all outer clothing.

For underwear I would choose something made of Nike dri fit or Clima lite I think it is called by Addidas. I run in shorts made of these fabrics and they wick well and do not chafe. Skins and Under Armor also make good products, I prefer a longer leg, not bikini cut because they cause chafing where they rub in the groin area.

I agree Merino is good but takes longer to dry and is a bit more problematic to care for.