Halliday & Matthiessen (2014: 336):
The difference between ‘doing’ and ‘happening’ derives from a different principle from the transitive one of extension–and–impact: ‘happening’ means that the actualisation of the process is represented as being self–engendered, whereas 'doing' means that the actualisation of the process is represented as being caused by a participant that is external to the combination of Process + Medium [i.e. Nucleus]. This external cause is the Agent.