You've understood how they work, now you must think about "when" they work to understand why they're there.
A turbo utilizes the exhaust gas to spin a turbine which which is mechanically coupled to another impeller on the intake side which forces air into the engine. As the engine produces more exhaust, the turbo spins faster and produces more boost until the set limit is attained. This limit is controlled by the waste gate , which "sees" the intake pressure and opens up when the limit is reached to vent off or bypass the exhaust gas around the turbo (vented to the catalytic converter or atmosphere), thus preventing it from spinning faster and creating more boost. It doesn't vent out the intake air.
Hence , the waste gate controls the maximum boost pressure (limited by how much your engine can take/ turbo rev limit etc).
Changing how much your waste gate "sees" can allow you to increase this limit (increase maximum boost). Look up - ball and spring valves, bleed valves, boost controllers.
A blow off valve, on the other hand, lies on the intake side and is meant to open up when the throttle is closed (by sensing engine vacuum). This vents out the pressurized intake air to the atmosphere. This is required because as you rev the engine up , the turbo spools up as well. The instant the throttle is let go, the turbo continues to create boost which now has no where to go. This causes the turbo to quickly spool down which creates a lot of impulsive stress on the turbo. Consequently , the turbo (now having spooled down) will take time to spool up when the throttle is re-applied.
Hence the blow-off valve protects your turbo by allow it to continue to spin (rotational inertia) and vent out the un-required air, when the throttle is closed. A consequence of which is reduced turbo lag eg. between gear shifts etc. Installing high flow blow off valves may improve turbo spool performance to a perceivable extent.
