you need to be more specific about the field you're asking about.
in some fields they might mean the same thing.
in other fields they might be carefully identified.
for example in my field...
as an instructor of meditative dance
my approach is nonverbal, mostly self-directed. it would include things like my philosophy (people can learn for themselves and play is a good form of learning etc.)
my method is structured sessions with meditative content--
a sequence of assigned tasks that lead the person to themselves.
the technique would be a specific exercise i would give ...
for example..."do one movement on the inhale and another on the exhale"
so as an instructor of linux
my approach is matter-of-fact, businesslike, professional, content-oriented. it includes belief like lab is a better learning
tool than lecture.
my method is lecture and lab
techniques might include using examples, going from known to unknown, going from simple to comples or big picture to little picture.
so as a parent my approach is unconditional positive regard with internal motivation. my approach includes the belief that my children can learn for themselves and make their own decisions.