Smoothness often comes from a large lightsource (i.e. a softbox or umbrella) The first link you posted isn't what I'd call crisp fashion photography so I'm not entirely sure what you're after.
Crispness comes from the lens, and from post processing. The balance switches as you reduce the image size. Don't be swayed by sharp looking but tiny images! For images downsized or the web e.g. 600x400px you can take an out of focus 16 megapixel image and make it look tack sharp!
As for fashion photography, you can't say it's more about the setup/capture, or it's more about the post processing. The truth is you need both for fashion photography. If either is not there it's very hard to make it up with the other.
One thing to bear in mind, you need a lot of space! Cramped indoor conditions give you very little control over your lights. Light bounces off the walls/floor and you get a muddy light with lots of different colours in it. What you want is a nice directional white light. A black walled studio is ideal, failing that shoots outdoors in a large enough space will suffice!