Depending on where you research these terms, they have been used slightly differently. Below is an example of one of my ready to hang paintings with a gallery wrapped edge.
Gallery wrapped canvas usually has a wider side edge than a studio wrap. Any staples or fasteners are on the very back and not on the edges. This type of canvas looks great even unframed and is considered ready to hang. The edges can be finished in several ways. One way is where the image of the artwork is continued on the sides as shown in the photo on the left or there can be mirrored edges or museum wrapped edges.
Mirrored edge gallery wrapped canvas shows a mirror image continuing onto the edges.
Museum wrap is a gallery wrapped canvas with the edge painted a solid color.
Studio wrapped canvas has a thin side edge, usually ½ inch or so and may have staples showing on the side. The edge is left unpainted. This type of wrapped canvas usually looks best framed before hanging.
Sometimes I use wrapped canvas with narrow edges that are painted so that the piece is ready to hang. Below are some examples.