There is no question that as technology has become a bigger part of our everyday lives, it has impacted how we do a number of things; how we shop, how we find information, how we communicate, and particularly how we write. There are a number of ways that online writing differs from traditional writing, and varies even more from platform to platform. For example, a person's writing on Twitter would be different then the writing on a blog. In addition to remembering things like subject matter and who their audience is, remembering these differences is very important if a writer wants to be successful in writing for the screen.
The biggest difference between traditional writing and online writing is that online writing is much more brief and concise then traditional writing. The most clear example of this difference can be found in the way news is reported. When writing for an actual newspapers, authors can be narrative and descriptive, and even stray a little from the actual topic if they choose, but when the news is reported on an onlineplatform it is much more brief and to the point. It is important for online authors to note that the internet has made most readers expect "instant gratification" as far as getting their information goes, if they don't get that from your writing, they'll get it somewhere else.
Another important point to remember though is that concise does not translate into sloppiness. Just because writing for the web has to be shorter, doesn't mean it should be more casual. Obviously the extent to which this rule applies depends on what you're writing for, but remain professional like you would if you were writing with a pen and a piece of paper; use proper grammar, punctuation, etc. Online it can also be tempting to clutter up your writing with different fonts, graphics, etc but these can be a turn off for readers and serve as more of a distraction then an aid.
Make sure to know your audience; do your research on both your topic, as well as the people you are striving to reach and impact with your writing. If people feel like you can relate to them, they're more likely to return to your site, even if you don't always write about the exact same topic. There are different studies that can help you prepare to make the transition from traditional to online writing as well. Just remember a few things: be brief, be specific, know your audience, and avoid sloppiness within your writing, and you'll be prepared to take on the task of writing for the web.