Web Design does share some traits that are found in Graphic Design, but that's because Graphic Design is a subset of Web Design. Some of the shared topics include typography, color theory, visual grammar (geometry, meaning and impact of shapes, balance, etc.), logos, branding, identity, iconography, symbols, and visual communication (communicating ideas and concepts from a client to an audience). I have not included grids because they are too different in print than they are for the web. It's vital that you do understand grid systems, but grid systems for physical layouts (such as books, physical canvases, and other prints) cannot be translated 1:1 to the web because a website's structure and reading mechanisms are significantly different. You spread information in a magazine or book on a fixed canvas from left to right, or right to left. You are limited to visually display content in a small, fixed layout, whereas on the web the information is spread in a "tree" format with an entirely different content hierarchy and flexible dimensions.
There are other differences in execution. When you create a magazine, you'll work with color theory, symbols, typography, visual grammar, and visual communication. You can't apply what you've done for the magazine to the web, however. A magazine has a much more clearly defined audience culturally, socially, and in terms of language, therefore it's easier to define color scheme, symbols, visual grammar, and format.
In Japan, to name an example, black stands for nobility and experience whereas in most Western parts of the world black stands for grief, death, and darkness. That's something you need to take into account when working with colors for the web because, unless a website is in Japanese rather than in English, your audience will be highly international, depending on topic, obviously. That wouldn't be much of a concern if you designed the same piece in Japan for a Japanese audience.
The same logic applies to almost all topics that these two professions share. The fundamentals are the same, but how you apply these differ quite a lot.