I don't understand that. What's the difference between "bribing" and "buying influence"? Is it about the time difference between when you give a politician money and when you expect something back?

It's the nature of the transaction. You are paying for a specific official act, that would be outright corruption.

Generally the money does not get you anything but an opportunity to pitch stuff to the politician, it's just an expensive way to become golf buddies.

There's a lot of things the politicians can help you with outside of their official duties. A senator chasing after your business partners visa issue is going to get it resolved within a day, without needing to wield any official power. This isn't corruption, corruption would be paying off the person making the visa decisions.

I get that if you come from a country with little actual corruption, this might seem like a distinction without a difference. It really isn't though, real corruption places a price tag on government officials doing (or not doing) their jobs.

I don't mean this in a dismissive way, because I appreciate your comment and you carefully set out a distinction, but it very much underlines what I'm worried about: that Americans are totally a-ok with corruption as long as it's done on a high enough level, to the point that it's openly discussed in the media and on internet forums and people do effort to explain to one another that it's not really real corruption at all.