This is a variation on the bay window. It is curved in an elliptical fashion as it extends from the building, unlike the bay window, which is angular. Another difference between the bay window and bow window is that bow windows do not reach the ground, and end above the top of the foundation. Bow windows first became popular in the Gothic era.
A carrol is a small bay window that is angular and does not extend to the ground. The carrol is an intimate space that can be used as a reading area or even as a closet. The carrol is an older architectural feature that was no longer used after the mid-1600s.
The oriel window is another variation of the bay window. It protrudes from the building but does not extend to the ground. The oriel window has more than one variation and can be rectangular, semi-octagonal or even semi-hexagonal. Within each side there can be more than one bay which is created by transoms as well as mullions. Oriel windows have decorative corbels or brackets which support them.