Do I need a Trademark AND a copyright?

I know how to file both but I'm not sure whether or not it is superfluous to get a trademark. The U.S. Copyright Office states that dramatic works (such as the web/TV show I produce) can be copyrighted. However, it also states that "Names, titles, short phrases and slogans" cannot be copyrighted, they must be trademarked instead. So would I need both to protect my TV show name and the show itself? Or would I just need a copyright? Please get back to me as soon as possible! Thanks.