A matrix business organization functions in an environment where two or more equally weighted functions must occur with concurrent activity and with which two or more elements of function must function at high performance levels. There are two or more centers of command (consistent with the number of organizational functions).
A team business organization allows for independent and freely creative teams made up of intelligent knowledgeable individuals who are able to and apt at sharing information and ideas.
The similarity is that both deal with multiple components of organization while the difference is that in the matrix there is strict chain of command while in teams there is unbounded freedom, though there may be group leaders.
A matrix organization structure differs from a team structure because in a matrix structure an individual employee reports to two different managers. For example, an employee will be required to report back to both the divisional and functional managers in a matrix structure. In a team structure an employee reports only to one manager.
A matrix structure maintains the vertical hierarchy but also establishes a horizontal relationship through functional departments while team structures work by eliminating the vertical hierarchy to some extent and maintaining cross-functional relationships.
The matrix and team structures are similar in the sense that they both require plenty of meeting time. In team structures members are constantly involved in discussions amongst themselves and their manager while in a matrix structure the employee spends a substantial amount of time meeting with the different managers.
Both structures are similar due to their level of flexibility. Matrix structures are flexible because they maintain both vertical and horizontal relationships and an employee can be reassigned as dictated by changes in operations. Team structures are also flexible because they work without bureaucracy which enhances the decision making process.
Matrix and team are two types of organizational structures and have their respective pros and cons.
Matrix organizational structure couples people based on their strengths in a matrix structure. The employees typically report to more than one manager, such as project manager and functional manager. This structure counters the silos seen in other organizational structures and combines the strengths of the members. Employees are distributed across projects as per their strengths and this allows easier information exchange & skill development and minimizes the weaknesses. The structure, however, suffers from confusion about responsibility distribution among managers, too many managers, etc.
Team organization is a newer form of organization structure and enhances collaborative work. People with relevant skill sets are divided into teams and are made responsible for particular task and report to only a single manager. Another example could be running each franchisee store (of say McDonald or Walmart, etc.) as a separate entity (managed by a team of workers). A number of organizations have team organizational structures and promote team work.