What's a bribe?

Yesterday morning I was thinking about bribes.

No, not offering one; but what constitutes a bribe?

And then yesterday afternoon I read about a Chicago doctor who was "... sentenced today to two years in prison for paying bribes to doctors to send patients to surgery centers he owns," according to the Chicago Tribune.

Sometimes, a bribe is thought of as a payment for a favor. For example, you get stopped for speeding and, when you hand the officer your driver's license, there "just happens" to be a folded $100 bill "stuck" under the license. If the cop becomes irate and demands, "What's this???", you just say, "Oh, I wondered where that had gone to."

On the other hand, if the cop smiles and says, "Slow it down, buddy" and sends you on your way, is that a bribe? Or is it a payment for being protected and served?

How did it work for that doctor, who had also been a Blagojevich fundraiser? Prosecutors said that the doctor "... has proved that he believes money buys influence.” Does it?

In fundraising for politicians, if a donor kicks a substantial amount of money into a campaign of a person running for office - and then later asks and receives a favor, was that money a "bribe"?

If the favor were never asked for or if the candidate rejected a request for the favor, the money would remain a political contribution. But how does it change, when a favor is called in?

And what is the legal position of the person who granted the favor, after having received a sizable contribution?