A line array system is made up of multiple speakers of different sizes and frequency ranges all connected together but at different angles forming an overall curve. Because of the different angles of the speakers, delays needs to be put in place so that there are no phasing problems between the speakers. This allows a tighter and very clean sound and since the sound is more focused it means that less sound energy is lost through the crowd so they are perfect for gigs in large locations.
A distributed system is when speakers are placed at each side of the stage at a concert. These speakers can either be speakers made up of tweeters and subs or full range speakers. These speakers are not as focused as the line array system as the speakers are omnidirectional and this means that the sound energy is more susceptible to being lost in a crowd so they are more suitable for smaller concerts. If they are used at larger concerts they will need to be backed up with fill speakers that have delays in place so people further back can hear as well as people at the front and also that the sound is in phase with the front speakers.
The fill speakers are used to fight against what is called the inverse square law. These means that every time the sound energy gets further away from the source it decreases in decibels in other words double the space each time the sound energy drops by 6db.