the difference between ESL and EFL is actually pretty simple.
If you are a Japanese student who is living in an English-speaking country and studying English, English would be your second (the's the 's' in ESL) language. Your first language, or mother tongue, being Japanese. You would study ESL in Canada, The UK, USA, etc
If you are a Japanese student who is living in Japan and studying English, English would be a foreign (that's the 'f' in EFL) language to you. You would study EFL in Japan.
In each of those two situations the needs of the student will be slightly different. The main difference being that the ESL student will need English to survive and conduct daily life activities. They might be in more of a hurry to master English since their life and livelihood might very well depend on it.
Of course, the grammar, reading skills, writing skills, speaking skills, and listening skills that English students need are the same regardless of where they study them. But there may be more emphasis placed on speaking and listening skills in an ESL class since those students will need them as soon as they walk outside of the classroom. ESL classes typically focus on functions (eg: requesting information, greetings, responding to invitations, etc) and practical, real-world situations (eg: at the post office, in the supermarket, at a job interview, etc).
In practice, unless you wish to teach at the college-level (highly unlikely unless you have a master's degree), most English schools in Japan will be delighted that you have any kind of TESL or TEFL credentials. Your manner, your character, your professionalism matter more to Japanese employers than any qualifications.
Wow. You've just gotten a whole of good free advice...
19 years teaching English (okay, EFL) in Japan.