language teaching vs pedagogy

language teaching and pedagogy both are nouns.

Word	Noun	Adjective	Verb	Adverb
language teaching	Yes	No	No	No
pedagogy	Yes	No	No	No

As nouns, pedagogy is a hypernym of language teaching; that is, pedagogy is a word with a broader meaning than language teaching:

language teaching: teaching people to speak and understand a foreign language
pedagogy: the profession of a teacher

Other hypernyms of language teaching include instruction, teaching.

language teaching (noun)	pedagogy (noun)
teaching people to speak and understand a foreign language	the profession of a teacher
	the activities of educating or instructing; activities that impart knowledge or skill
	the principles and methods of instruction