There is often much confusion surrounding these acronyms but essentially they mean the same thing.
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TEFL = Teaching English as a Foreign Language
TESOL = Teaching English to Speakers of Other Languages
The above are generally used interchangeably, however, TEFL is most commonly used within the UK and TESOL is usually preferred in Australia and the USA. Although some countries may favor one acronym over the other, it is important to remember that a TEFL certification and a TESOL certification are exactly the same thing as the training involved is identical.
Although TEFL and TESOL training courses are identical and the acronyms are generally used interchangeably, there is a technical difference between the two. The general perception is that speakers of English as a foreign language live in a non-English speaking country, meaning they don't need to speak English on a daily basis and are usually learning the language for travel, business or simply as a hobby. In contrast, speakers of English as a second language live in an English speaking country, meaning they do need to speak English on a daily basis for work, socializing, shopping etc.