Historically, the difference has been explained by whether the person taking it believes in ‘divine mercy and vengeance’, as an oath is believed to ‘invoke divine vengeance’ if the person does not speak the truth.
An affirmation is a solemn declaration of the truth without reference to anything divine, so it may be appropriate if the person is an atheist or agnostic (and where statutory provision permits its use).
An affirmation can also be used if it is not practical or convenient to accommodate the formalities required by a particular religious faith.
