I understand your concern and agree with you that it is preferable to have a teaching qualification that is accredited.
For this, you need to check whether it is moderated by an external body or not. An example of this in the UK would be UCLES (University of Cambridge Local Examinations Syndicate), I'm not sure what the US equivalent is.
People tend to use TEFL as a blanket term in the UK and TESL in the US. In the UK, we would use TESL to refer to a learner from India (for example) where English is commonly used as a working language but is not the first language of that country. Techniques and activities for teaching these students are different from teaching an Italian learner (for example).
For a fuller discussion of the differences, you can look at the Teflnet webpage, go to quick links and look under teacher training. There is a TEFL course database on this website and also on http://www.englishclub.com