esl Methodology vs esl approach

[gladrod]

What is the difference between language teaching esl methodology and language teaching approaches.

[Mister Micawber]

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Nothing necessarily, but an 'approach' would be the general attitude toward the nature of language teaching and the ways it should be pursued, while the 'methodology' would be more detailed methods, ways of teaching e.g. listening, etc.
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[ESL Teacher]

I wonder if you meant the "language experience approach" vs. ESL methodology. If so, then the difference between ESL methodology and the LEA is that the former is an umbrella term that includes the later, among many other methodologies.