An old school friend asked, so I thought I would post an answer, this is to the best of my knowledge correct but I am sure that those that know will post a comment
A 'Josher' is the style/shape of the bow, it was first designed and built by a Joshua Fellows.
He was part of the company, Fellows, Moreton and Clayton, one of the more well known companies trading on the canals.
A true 'Josher', which mine is not, has a subtle double curve, difficult to see in a photo.
'Birmingham square' is to do with the shape of the hull, the majority of narrowboats hulls slope inwards as they go down but a 'square' as the name implies, are more vertical, you gain a few inches in width.