DIFFERENCES
Lift-Dumper: This is very rarely used, and when it is, usually always in an emergency. A lift-dumper is where the device is fully deployed in mid-air. ​
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Speed Brake: This is often used when an aircraft begins its descent to an airport. A speed brake is where part of the device is deployed in mid-air or on approach to an airport. ​
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Spoilers: These are only used on the ground during nearly every landing procedure. The spoilers are where the device deploys fully as the aircraft touches the runway.
EXPLANATION
How spoilers and speed brakes work is very simple: they create drag. When the device is deployed, it creates a shield against the wind, stopping the wind from going any further, thus creating drag. This also decreases lift, which often causes the aircraft to descend.
USEFUL PICTURE
A close-up of the spoilers/speed brake system on an aircraft.
USEFUL TIP
You can arm the spoilers in mid-air by pressing Shift + /. On touchdown, they'll deploy.