To pick is an act or the right of selecting something from a number of alternatives. To choose is to decide on a course of action. Though 'Pick' and 'choose' are often used interchangeably.

Pick has more uses. One of the meanings of pick is same as choose, but pick also has another meaning: He picked the spinach from between his teeth. And pick also combines with several different particles to form a variety of phrasal verbs: pick on, pick at, pick up, pick through, etc.

There is no difference. "Pick" might be very slightly more informal.

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