Because bribery and extortion have many elements in common, it is easy to misconstrue one as the other, but important not to. Both are criminal offenses and both involve the exchange of money, property, or services, but the manner in which the exchange occurs and the parties involved often vary depending upon the nature of the crime. A charge of extortion, for instance, need not involve public officials to be made, whereas bribery as a criminal offense involves those employed by the Government, mostly, along with certain clear provisions for cases of bribery in business.
The primary difference depends on the nature of the relationship between the person receiving goods, services, or money, and the person giving them. In extortion, the receiver is the initiator of the transaction, as opposed to the giver. But in bribery, the bribee could still be the initiator, instead of the briber. The key difference, then, is that in extortion the extorting individual, the receiver of goods, is not offering anything to the extorted individual, the giver.
The receiver is actually making a threat towards the extorted party, threatening to perform a certain action that will harm the extorted party unless the extorted party gives the receiver whatever the receiver requests. Bribery, on the other hand, might involve the bribed individual asking for a bribe from the bribing individual, but in general, the bribed party will then do something in the favor of the bribing party.
As an example, take the following: Government official Albert tells businessman Bob that in order for Bob's company to get an exclusive Government contract, Bob needs to bribe Albert. This is not a threat; Albert is not saying that he will harm Bob if Bob does not give Albert what Albert wants. Albert is instead simply saying that he will deny Bob the good that Bob seeks, unless Bob bribes Albert. In this example, Albert is the bribed party and Bob the bribing party, despite the fact that Albert may have initiated the contact.
But in extortion, the relationship between the two is quite different. Businessman Bob threatens to reveal Government official Albert's affair with a woman other than his wife unless Albert gives to Bob the exclusive Government contract. In this case, Bob is genuinely threatening Albert with harm, specifically harm to Albert's reputation, unless Albert does what Bob wants. Bob is not offering to give Albert anything positive; if he did, it would be a bribe. Bob is instead, essentially, offering to withhold doing something negative if Albert does as Bob asks.
The earlier mentioned difference between the two is also quite significant, in that there need be no Government employee involved in an extortion case. There does need to be a Government official, or some other specifically mentioned instance of unlawful bribery involved in a bribery case.
Extortion could occur between two businessmen and still be a criminal offense, whereas bribery is primarily focused on the bribing of Government employees or bribing by Government employees. But the most important difference is the difference between a threat to do harm in extortion and an offer to do good in bribery.