La vareuse est la version "chic" de la chemise

...meaning that the smock is the chic version of the striped shirt...  But I don't know about that; I guess in times when both were solely worn by seafaring men, there may have been some truth in that, but since Chanel and Gaultier it may well be the other way around.

Either way, both share a very similar history and use. The smock (or vareuse, in French) is a long-sleeved tunic with a front slit for easy dressing, originally made from worn out sails, sewn by sailors.
The original fisherman smock is made of a strong woven cotton material and has two characteristics : a front button closing the tunic from the inside and one or two inside pockets (so one couldn't get caught by anything aboard the ship). 

The smock originates, like the striped shirt, in Brittany, but also has a long history on the British Coast - made in the fishing-towns of Essex and Norfolk.

And, much more than the striped shirt, this smock was adopted by navies around the world. Likewise with painters and potters - the smock proved to be an ideal garment for work with paint and clay (painter's smocks often have a number of outside pockets sewn-on).