There are multiple types of missions in this game. First of all, there are story missions and side missions. Story missions are grouped in storylines, while side missions are not required to finish the main game but rewards quite generously upon completion. Some story missions are timed while some are not.
Also, there are random missions. These are generated randomly. A particular survivor in your game will be randomly picked and deployed to a certain mission. Different types include Search and Rescue, Zed Hunts, Ally Assistance, and Infestation Clearings.
Take note that you can be assisted by your survivors on your own missions, and they are very useful to say the least. You cannot manually pick characters though.