Design is the basics of a web layout. It can be where a column sits at on your page or where your text is located and if it word wraps or is a set width. Style is almost a sub categorey of design. Ya it allows you to change how a web site looks but its in the major details when it is style.
Style is the small things like what text format you have and what is your color scheme for the whole web site. Style could also include things like flash. What does your web site do? Does it have any motion to it or is it static. Anything that you do with flash could be considered style.
So design is considered the basic format of a site while Style is the small things that make a site a little more unique. These days many people want almost all style with little relative thought to the basic design layout.
