Preventing: The name is saying, prevent to something happen. For example some companies make some background checks, with this they can find out if a person is getting some economics or law problems and avoid hire somebody for a risky position.
For example, if somebody is getting economic problems and it is managing money or secrets, this person could get some money or sell some secrets, the background check will prevent to hire a person for this position.
Detective control: This detect something when is happening or after happen, like the intrusion detection system in a network.
Corrective: Correct some situations, like the antivirus detect a virus and try to clean the file or quarantine it.
Recovery: This control recovery after an incident, for example after a hard drive fail, or user delete some data, or a virus damage data, all this situations require to restore from backups, install OS, reconfigure, etc, etc to restore the functionality of the system or availability of the data.
Deterrent: This deter a user to do something, for example when you see signs like "Smile you are on camera" or "beware of dog" or "security on duty" etc. The user/attacker/person avoid to do something because he/she doesn't want to be catch or get problem in that situation.
Compensating: This compensate or complement the weakness in one area to full fill the missing part or make it stronger.