TESOL, TEFL, TESL are basically just names- I wouldn't worry about them as terms. In the US, they use
ESL, but in Australia and the UK ESOL is more popular.
With distance learning, I'd be very careful about these courses and check them out very carefully- there are some dodgy ones and be very wary of the accreditation. Basically, ignore many of the promises of guaranteed work and look at the small print. In terms of not being a graduate, that depends very much on the local law of the countries- some insist on teachers being graduates, others don't. In some countries, just being a native speaker is enough, but this locks people into a very fragile system with few prospects.
My advice would be to try to find a part-time course with a reputable bricks&mortar place offering courses accredited by an offical body (many online providers have set up sham accrediting bodies and pass themselves). A qualification that dosn't carry much weight will lock you out of all the reputable schools, unless you happen to be there the day they've lost a vital teacher, and these are the places that pay better and offer more security. There are areas of the world that are pretty much bandit territory in
ESL. The US government issued a recommendation a few years ago about not going to Korea because they were getting so many horror stories about teachers getting ripped off. I really do think that it is worth getting a proper qualification.
These people might be worth checking out for advice:
http://www.tesl.ca/
If you are thinking of a course, feel free to post again and we'll offer our opinions on it.