Go on + gérondif veut dire continuer l'action du gérondif.
Exemples
- He went on speaking for two hours.
- I can't go on working like this - I'm exhausted.
- Even after I apologized, he went on being angry for another month.
- The show will go on playing through the end of the year.
Go on + infinitif veut dire passer à l'action suivant, qui est le plus souvent l’étape suivante d'un processus.
Exemples
- After introducing her proposal, she went on to explain the benefits for the company.
- John Smith worked in local government for five years, then went on to become a Member of Parliament.
- After making dinner, I went on to set the table.
- When you're done with your soup, you can go on to serve the main dish.