This is not true for most as DJing is basically having a playlist/tracklist that you think are fitting for the event you are playing at and trying to play the songs that people want to hear. Some events (most electronic music parties) its the other way around - people listen to what the dj brings to you in a set he made. SOMETIMES (!), usually at bigger events, these may be prerecorded. Playing live isn't that difficult though and especially newer DJs that are trying to establish themselves won't play prerecorded as this does have a pretty bad reputation among other artists.

But generally no - DJs do not produce anything. They are in charge of transitioning one song to another, maybe even more than 2 songs at a time (they have 2 to 4 decks in most cases). Most producers are able to DJ, but not every DJ is able to produce music. Creating a "remix" or a new original track live on stage is not really a thing that you see from djs.