What's the difference between Kontakt and the Kontakt Player?
The free Kontakt Player is a light version of Kontakt that's designed to only play sample libraries that license this software from Native Instruments. These libraries are usually referred to as "Player" libraries, compared to "non-Player" libraries which don't license the free Kontakt Player.
The primary reason that some libraries license the Kontakt Player is so that users don't need to own the full version of Kontakt to use the library. Due to the cost associated with licensing the Kontakt Player, it's uncommon for free and inexpensive sample libraries to license the Kontakt Player. If you load a non-Player instrument that doesn't license the Kontakt Player in the free Kontakt Player, it will appear in a time-limited demo mode.
However, the full retail version of Kontakt can play both Player and non-Player libraries. It also offers additional features such as being able to edit instruments as well as create your own instruments—a useful option even if you only need to quickly map a few samples to make a playable patch.
If you're unsure which version of Kontakt you have, it's easy to check. The full version of Kontakt simply has the text "KONTAKT" in the upper left corner of the interface, while the free Kontakt Player displays "KONTAKT PLAYER" instead.