It would also be perfectly legal to hire a politician or regulator who advanced your interests once he's no longer in office. There is, in fact, a revolving door between many industries and the agencies that regulate them. But you can't explicitly promise these individuals a job while they're still in office or you committed illegal bribery. A politician also can't sell a Senate appointment (as the governor of Illinois infamously tried to do after Obama was elected president) but he can give it to one of his political allies as a favor and reasonably expect that the favor will be repaid in the future.
Of course, these differences aren't particularly meaningful in reality but they're very important under the law and anybody who is stupid enough to execute their bribes the wrong way will probably be punished for bribery even though it would have been perfectly legal if they'd done it the right way.