There are three types of gaming modes. The co-operative mode means that two or more players co-operate towards a shared goal. The opposite is the competitive mode where multiple players compete against each other. Team mode is a combination of the the co-operative and competitive modes.
Co-Op, Competitive, Teams
Multiple players per console
Online gaming support
Two or more players use the Internet to connect the gaming consoles. The opposite is local gaming where no external network is required.