Lobbying and bribery are not literally the same thing, or not technically but they can be done for the same purpose. Bribery is always considered illegal and comes with a criminal price tag, while lobbying is not illegal but perhaps should be, according to many.
Bribery is considered to be a sale of power, in essence. Lobbying is more like an influence of power in a political realm which is accomplished by giving or offering contributions that ultimately affect outcomes of a political nature. Bribes are usually smaller amounts when they are compared to lobbying contributions but not always. Although the two are not the same, in reality, they are very similar. One is legal, however, and one is not. That makes a huge difference.