these are all fairly dated terms now or so i believe as they date back to times when the cassette tape and the record where first in vogue. A mix tape would be a selection of songs recorded onto a tape from various artists, often by a spotty teenager for a young lady he was hoping to wow with how great his taste in music was, unfortunately as a result he would generally be "friend zoned". It also refers to more professional tape mixes such as the popular "now"series.
(for those of you lucky enough to be young enough to remember using a pen to rewind a cassette tape that had been chewed by your tape player for the 16th time that day)
EP stands for extended play and is an album which is longer than the old CD single but not as long as a full album, normally 4 or 5 songs. Often these were released by artists in between albums to maintain interest in their music whilst they were touring or having a long recording break between full albums. The Beatles magical mystery tour was probably the most famous example of an EP.
Conversely, an LP is an abbreviation of long play and is what would be considered a full release album, generally 10 songs +.