Sampling (taking a track from another song and not changing it) technically infringes copyright because it violates the original artist's exclusive right to reproduce the work. Similarly, remixing (taking a track in whole or in part and changing the melody, rhythm, etc.) infringes copyright because it violates the original artist's exclusive right to adapt the work. These rights are essentially the same, however remixing is a bit harder to prove because a person making a substantially different song has a "defense" and doesn't legally infringe the song.

Covers (making a similar but distinct version of the same song) are interesting because there's actually a statutory exemption that permits a person to make a cover once the original artist has already authorized the distribution of a recording. The cover artist can be required to pay royalties to the original artist, however.

Interestingly, though the law is pretty clear, what's less clear is enforcement. Some artists welcome people remixing or sampling their songs and don't enforce their rights, whereas others vigorously enforce their rights.

Disclaimer This is a very general overview of a complex topic. If you're thinking about sampling or remixing a song, you should consult an actual attorney, as there are numerous factors that can impact whether you could be liable for infringement.