They are literally not the same. Lobbying is when you try to convince someone and influence their voting/law making etc. Bribing is paying to set the prioritising and define what is important. However, bribing may also be done for noble causes, prohibiting bribes is limiting the opportunity for all kinds of actors to ensure their cause isn’t deprioritized in a harmful way.

They’re literally the same, we just legalized using money to set the agenda and made a new word for it.