Matrix metering means it takes 95% of the frame into consideration for shutter speed as center weighted will pick out 8-16% of the focus point and center is just the focus point for shutter speed
That depends somewhat on the brand/model of camera you are using. Your camera's user's manual will describe how exactly how the different metering modes work for your camera.
Matrix (Nikon) and Evaluative (Canon) metering looks at the entire scene, and in the scene averages the light level.
Center-weighter metering also looks at the entire scene but assigns a 75% weight to the middle of the scene and the other 25% to the rest of the scene. How much of the cnter is considered by the camea is often adjustable.
Partial metering is a Canon option and how much is partially metered is also often adjustable.
Spot metering is the most accurate metering mode and only samples 2% to 5% of the scene. Again camera brand/model determines exactly how Spot metering can be used.