Print Design vs. Web Design
As a designer trained in fine art and traditional graphic design (of the gouache-color-studies-and-hand-tooled-type-sort), my transition from dabbling in print to a world of divs, navigation, accessibility, and Arial-Verdana-Times limitations was not effortless by any means.
Designing for web is an interesting field; the diversity of websites out there is so great because while many novice designers struggle with layout, color, and typography because they lack training/awareness of these fields and lay out text as one would in a word processor, others put a lot of consideration into creating a navigable design with strong composition, color balance, and attention to detail. This creates the difference between a web page that is, as Joe Gillespie calls it, not an end result but only the messenger versus a fully integrated showcase of design, information, and accessibility.
While certain design skills and sensibilities are transferable from print to web, others are actually inappropriate when it comes to creating a usable web interface. I have found that in every discipline of design, there are ways to adapt training from one medium to the other, keeping in mind the differences between a tangible piece and what is displayed on a 1024x768 (or otherwise) monitor.
Composition
Considerations of composition for a printed piece are distinct from those for a web page. The negative space resulting from a blend of layers of ink have very different qualities from the negative space of an area of pixels of the same color. The blank slate of a page of a book with its implications of orientation, physical size, and flow of information within a multi-page chronology is very different from a blank web page that will be viewed in multiple resolutions, by viewers with certain expectations of such things as navigation placement, with information processed in a continuously scrolling (generally) vertical format.
A designer must be aware of the unique experience of moving between sections/pages of a medium; whereas this is linear in a multi-page booklet or brochure, there exists a network of interlinked pages in a website, all containing various stages of interactivity with the viewer, and this affects the ultimate design experience.
Typography
The treatment of type is another area that differs between the two disciplines. While it is of course always important to be attentive to the anatomy of a typeface and the minute spaces inside and in-between letterforms, the way that text functions and its interpretation are highly dependent on the medium.
Primarily, the use of HTML text in web design places great restrictions on the placement and appearance of type to begin with, and this immediately separates the aesthetic elements of the page from the HTML text that conveys content and is used for search engine optimization.
Conversely, on a printed page, the typography can be fully integrated with the aesthetic elements, and the designer has full freedom in terms of type orientation, layout, spacing, font type, etc. The functionality of text in print also inherently differs from that on the web; letterforms can act as aesthetic elements on, say, a poster, where they can be layered on top of each other, oriented in different directions, and still communicate their purpose. Whereas, if the type on a website was not laid out in a straightforward way, the page would be unsuccessful.
Stressing legibility, comfortably-sized font, and organization of a page rises higher on the list of priorities in design for the web. Perhaps this speaks to the idea that users come to websites to discover information. Whereas, printed pieces have the freedom to linger somewhere between the aesthetic and the communication of information.
Color
The complex study of color theory is universally beneficial in the design field, regardless of medium. Subtleties between hues and tones as well as the rich and delicate relationships between colors are essential for any sort of designer to appreciate, in the name of the tone and emotional evocation of any design. However, the effect of color on the web does differ somewhat from color on a page.
Working with pixels of color and hexadecimals gives you a certain precision and control over the final display that you lack when working with printers and spot colors yet the visceral quality of exploring colors by physically mixing inks is of enormous value. The certain reverberations between two juxtaposed colors of paint may or may not be reflected in two juxtaposed objects on the screen.
In conclusion...
Ultimately, while there are many facets of design that are universal regardless of final output, there are also differences between print and web design that must be appreciated. As long as one approaches the shift between mediums with the understanding of its unique qualities (the insight that a printed piece can't just be slapped on the screen and have a left navigation added to it) and as long as one is aware of the boundaries of each, he or she can be a successful designer in both worlds.
Personally, I am obviously not claiming to be a master or a success in either field, but (and my slight obsession with theory clearly comes out here) I think it is of great consequence that designers are aware of the anatomy of their designs and the intricacies of their mediums. As Jakob Nielsen maintains, websites are largely user-based interfaces where communication of information is prevalent, and this should at least be noted somewhere in the designer's head if not at the forefront of the process.