The art of taking two records, and altering the speed of one record so that its beats run in synchronisation to that of the other record. By doing this a DJ can run two songs at the same time and switch between the two to give the audience the illusion that it is the same song. This can (and is) repeated throughout the entire set, delivering to the hours of continuous music without a break, often making it hard (if not impossible) for them to detect the end of one song and the start of the next.
Mixing is the art of creating new sounds and songs by mixing two songs together (i.e. playing them at the same time).
There are many different ways to mix two records, depending on the genre of music you are mixing, the venue and audience you are mixing for, and your own independent style. Beat-matching is a fundamental aspect of mixing which underpins the DJs ability to mix, as no matter how good the mix, if the beats arent in line it will sound awful, and could bring your career to an abrupt end.
Some of my favourite moments, as a DJ and as a spectator, have been while a DJ has had two tracks running together creating a completely new sonic experience. Equally, some of my most boring moments have been listening to DJ Synchrobeat treat us all to a long running mix that demonstrates a skill in keeping two tracks together but does not actually go anywhere or serve up any treats for the dancefloor to digest.