So this is one of those questions which causes a lot of confusion especially when you’re looking for a training certificate. Often they are used interchangeably (sometimes incorrectly too) Hopefully this will answer the question.
TEFL Teaching English as a Foreign Language.
Often, but not always this happens in a country where English isn’t spoken as a first language. In British English it’s often used as an umbrella term for teaching non-native speakers.
TESOL Teaching English to Speakers of Other Languages.
TESL Teaching English as a Second Language.
These often refer to teaching English to people who are learning English in an English speaking country. So these qualifications would be more useful for people thinking about teaching English is places like the UK, the US, Canada, Australia and Ireland.
This is a TEFL course run by Cambridge English and stands for Certificate in Teaching English to Adults and is probably the most recognised and the most expensive course that you can do.