There's a bit of crossover between the two, but web designing is basically a graphic design function and web developing generally implies some sort of programming.
I also build a lot of sites where I create the graphic elements myself...AND do the programming necessary to make my design into a website. This is a combo of design and development, and is the part of my job I most enjoy. Here's a good example of a site where I designed and coded the whole thing from start to finish: http://www.watchmakertothestars.com/
I think web developing is generally more difficult than design, although there some big exceptions!