I always tend to compare things to other things, so let me begin with that. If having an online profile is like riding the train then owning a website is like owning a car. You can still have online profiles anywhere you want, but it all leads to one main page about you.
Is it good to have an IMDB profile? Yes. Is it good to have a LinkedIn account? Yes. Do twitter, tumblr, facebook and other online profiles help? Of course, but can you really "own" any of them? Not so much. Online profiles are there for anyone to use in a specific manner. They usually all look the same and can be easily researched.
So what exactly is online presence and what does it have to do with online profiles? Let me answer your question with another question. Have you googled yourself lately? It may sound vane, but really you're just seeing how your name is represented online. When I google myself I see LinkedIn, YouTube, Facebook, Twitter and Pinterest. Those are my defining social media points for online presence. But do I really want my personal Twitter or personal Facebook account to define me as a professional? Absolutely not. That's why my own website is there as well. With good S.E.O. practice and proper application of keywords we can push the results higher up the list and make your own website shine through, so that when people search for you they don't end up on your Twitter account, reading your thoughts about the last Survivor episode. They end up on your website, browsing through your portfolio and learning about your abilities. That's what online presence is all about.