Recent positions of all ships which carry an AIS transponder are lastingly being recorded via the MarineTraffic network of AIS-receiving stations to its database. This way, thousands of vessel positions are available at any given moment. However, if there is no fresh position of a vessel for a long time, this vessel is removed from the Live Map until an updated position of her becomes available.
Note that you can define the age of the Last Position Received (ranging from current positions up to a year ago) of any vessel and be getting the relevant information on your screen by using the Advanced Vessel Filters.
The colour of each vessel icon notates the subject vessel's type. You may use the Live Map Toolbar Filters to choose which types of ships you prefer to be displayed on the Live Map (the Filters section may also serve as an easily accessible reminder, in case you have not gotten accustomed to the icons' colours yet).
Keep in mind, that the vessel icons also represent the status (moving / stopped) of the corresponding ships. Also, the direction that each (moving) vessel's icon is pointing to, indicates the subject vessel's actual heading.