TEFL = teaching/teacher of English as a foriegn language. That means the learner does not plan to live in an English speaking country as a long term resident, i.e. as an immigrant. Rather they will use it to study or in their work or life, but generally in a non English speaking country.
TESOL = teach(ing) English to/for speakers of other languages. This includes EFL (see above) and ESL (English as a second language - this is for immigrants to English speaking countries)
Most teachers will work in the EFL industry. ESL is generally a domestic government or sub-government 'industry' as opposed to the EFL industry which has profit making schools/businesses the world over.
CELTA = Certificate in teaching English to speakers of other languages. This is an actual qualification (not a general industry acronym) that belongs to the University of Cambridge.
As to the comparison of qualifications it's reasonably simple. CELTA is recognised the world over as the basic requirement for EFL teachers (not for ESL). In some places it may not be prefered, but it is without question the most recognised qual. Many countries will have another qual, such as the CERT IV in TESOL in Australia. However, most employers will prefer the CELTA.
There are higher level quals, such as the DELTA (also Cambridge) and Masters degrees. These later tend to be more up to date in terms of methodology, however, they rarely do anything to help the prospective teacher perform or even survive in the classroom.
I'd suggest that those above who have suggested that CELTA isn't the way to go have either something to sell or an ego to protect.
To be totally transparent, I have been a teacher (EFL) for 12yrs, an employer (DOS), and a trainer - both CELTA, a 'TESOL' certificate, and CERT IV in TESOL. I also have a DELTA and a masters.
My advice? Do a CELTA. If you're not sure, call a range of schools in the countries you want to teach in and ask what they want.
Good luck.