A quick recap on United States intellectual property for my students.
Copyrights and patents are monopolies granted in law to creators so as to encourage the creation of ideas and expression. Trademarks protect a "sign" (e.g., a logo or terms) associated with products or services. You can assign, transfer, or license all of these rights to others.
Patents protects ideas/inventions and limits others' abilities to make, use, and sell things that depend on those inventions. You have to register a patent and it lasts twenty years, after which everyone can use it.
I don't think Taylor Swift has any patents -- unless she's invented something!
Copyright protects expression (or "work") and limits others' abilities to make copies, create derivatives, and perform or publicly display works. It originally lasted 14 years, renewable to a total of 28 years, and then would revert to the public domain for everyone's benefit. Over the years, it's been extended and now is life of the author plus 70 years. Some rightfully ask how does such a long term encourage creation? It doesn't, but companies like Disney don't want to give their copyrights up. You have a copyright in a work of expression as soon as you make it and you can register it so you have a stronger case in court. Free culture (like Wikipedia) and Creative Commons licenses make it easy again to create things that other people can use relatively freely.
Because Taylor Swift writes (or co-writes) most of her songs, she has has the copyright in the music and lyrics; Swift also has the copyright in her actual performances (e.g., recordings or videos of a concert).
A trademark is a recognizable sign associated with a product or service -- you can think of the "brand." You can make a "common law" claim (TM) or register it (R); a registered mark makes a stronger case in court. These can last indefinitely, but marks can become "generic" should they not be strictly limited to products and services from the claimant.
Swift, like a number of other big artists, has filed for trademarks on fragments from her songs. This would limit others' ability to use those lyrics in association with a product or service. Hence, no one but Swift could sell "this sick beat" brand t-shirts or hats. But she doesn't have a copyright on that expression (too small; not sufficiently original) so you could still use that phrase in speech or writing. Of course, just because she filed for the marks, doesn't mean they'll be approved; and even if they are, it doesn't mean they'd stand up in court. Trademarks based on her name would be much stronger than any of these phrases.