Designing for the web introduces a whole host of new variables, limitations, and opportunites that aren't present in print design.
While print design usually means designing for fixed layouts where the designer knows exactly how the content will be displayed to users, web design requires taking into account the fact that users can be viewing their content on a variety of devices, each with different pixel densities, color profiles, and screen ratios. Often times, this also means designing for fluid experiences, where designs must be able to react to changes in screen size and page events, presenting new design challenges.
Futhermore, the technical constraints are higher in designing for the web, where the designer is expected to know what is and isn't possible with current technologies. For example, web typography is still in its infancy: many standard typographical tools aren't available or easily accessible, and some foundries still do not license their typefaces for use online. In addition, bandwidth constraints require designers to also take things like filesize into account, sometimes restricting design opportunities in the name of a better user experience.
Designing for the web, however, also brings with it interactive elements that aren't present in print design, which offers up many new possibilities, but creates more work for the designer. For example, it opens the door to adding animations and transformations to page elements, but that also introduces user-experience as a new goal for designers to worry about. Whereas with print design there is usually little user interaction, on the web it becomes a primary concern to the designer, creating a new lens through which they must look at their work.