If you've already completed an ESL teaching certification, you may not need TEFL to teach online or abroad, but the requirements can vary.
If you are a CELTA certified instructor in good standing, you will likely not require a TEFL certificate and may use your existing CELTA certificate to apply to ESL teaching jobs online and abroad.
TESL qualifies you to teach within an English speaking country.
In some cases, a TESL certificate will also be accepted for jobs abroad or online, but it may not be suitable. You may still be asked for or benefit from a TEFL certificate.
TESOL stands for teaching English to speakers of other languages. It is a broad term that can be used for courses that only qualify you to teach overseas, or qualify you for both teaching overseas and at home.
In general, if you have a reputable TESOL certificate that has 120 hours or more of training and your certificate clearly states you have completed 120-hour course, you will be able to use your TESOL to teach overseas.
If you have completed less than 120 hours of training, your certificate will not qualify you for online teaching and will limit the countries in which you can teach overseas.
If you'd like to use you TESOL to teach within an English speaking country, you'll typically need 250 hours of training plus 50 hours of teaching observation/practical teaching experience.