commence
This is more formal and often used in official or ceremonial contexts.
- The graduation ceremony will commence at noon.
- They will commence the construction of the building next month.
begin
This is used in general situations where you want to mention the start of an action or process in a straightforward and neutral manner.
- We will begin the meeting at 10 AM.
- She asked him to begin his homework.
start
This is a versatile term, suitable for most informal or conversational contexts to indicate the beginning of something.
- We can start the movie now.
- He decided to start his own business.
initiate
This usually implies initiating something new or complex, often with a sense of formality or technicality.
- The company plans to initiate a new project next quarter.
- The doctor initiated a series of tests to diagnose the condition.