I think it is quite easy to distinguish between new and old media, but I can't say the same about distinguishing between the various new media technologies. This is a long read, but only because I think it is best explained with many examples. Old media tends to be static, non-interactive, slower means of communication and less easily produced and distributed. While new media tends to be more dynamic, interactive, quicker and easier to produce and distribute.
Let me explain further on those concepts. For old media such as newspapers, or TV the content is the same. You can read the same newspaper over and over and the words printed on the page will not change. When re-watching a movie or episode of TV, it will play the same way every time. While for new media, the content can change. An example being amazon.com's product referral system. If you click on a certain product or purchase a certain product, the website will make recommendations based on those products you viewed or purchased. A another example would be mmorpgs. When you play an mmo, every playthrough will be different. Like choosing a different character, learning different spells, using different items, and etc.
Which brings to the next concept of interactivity. Using newspapers and TV again, you can only read the newspaper and watch TV episodes. And that's it. While for video games, you have to command your character to do every action. For websites like blogs and forums where you can make posts and share your thoughts, opinions, and pictures. Or wikis where you can add or edit pages. In old media websites, all you could do was read off the page and nothing else.
The next concept is speed. For old media, its much slower. Sending a letter through the post office will take days to weeks. If you write something for a newspaper or magazine, it takes time for them to be printed, distributed, then customers purchase them and read them. While for new media, its much faster and in some cases instantaneous. Such as a blog, all you have to do is click the "Publish Post" button and your writings are instantly available to read on your blog. Anyone and everyone can read it right away. It doesn't have to be distributed to stores, or require a release date like newspapers. Going back to the post office mail example, new media technology such as email or text message lets you send messages to a person anywhere almost instantly. And they can respond right away. So you don't have to wait weeks for a response or worry about your letters getting lost in the mail.
Lastly, the accessibility of the media technology is a great distinguishing factor. For old media, it is difficult and expensive to get an article published, or produce a film and have it aired on television or at theaters. While for new media, anyone can write their own articles and post them on blogs. As youtube as shown, pretty much everyone can produce their own films and distribute them online and reach a massive audience.
Hopefully I have explained the distinguishing factors between old and new media sufficiently enough so you the reader can easily tell the difference between old and new media.