As nouns the difference between wainwright and farrier

is that wainwright is (climbing) any of the 214 fells (hills and mountains) described in a wainwright's pictorial guide to the lakeland fells (1955–1966), often visited as a form of (peak bagging) while farrier is a person who maintains the health and balance of the horse's feet through the trimming of the hoof and placement of horseshoes.

As a proper noun wainwright

is from someone who built wagons.

As a verb farrier is

to practise as a farrier; to carry on the trade of a farrier.