If there is proof that they have given millions of dollars, this will go to court, as that is illegal. Lobbying is not bribing as I pointed out in my initial reply. Lots of different groups and organisations use lobbying to make their concerns heard. Just because this is a case we don’t like, does not mean lobbying has no purpose.
They are literally not the same. Bribing is when you try to give something in exchange for voting/law making etc. Lobbying is convincing why prioritising is important. These can be selfish reasons, like in this case. However, lobbying may also be done for noble causes by a wide range of NGOs. Prohibiting lobbying is limiting the opportunity for all kinds of actors to argue their cause.
I agree that both their objective lies in changing regulation. Doesn’t mean that they are the same, however. Which OP stated. And I wouldn’t say it is the only difference, rather the difference between the two.