The Burtray, Walnut and Water Sprite outboard motors were essentially all the same motor and were made from 1907 - 1909, except for the Water Sprite was made only in 1910.

Be sure and check the entries for Walnut and Water Sprite for more pics.

The Burtray is a single cylinder outboard sold by the Burtray Engine Works of Chicago, Illinois. I believe it was a badge motor made by the Walnut Machine and Brass Foundry Company of Toledo.

While I have found many ads by the Burtray Engine Works selling the Water Sprites, I have none of Burtray selling the Burtray! I think it is possible the company decided that Burtray wasn't a name that helped their motor sell. In the early 1900s many folks still were not comfortable with the new technology of internal combustion engines, so a more fun name that projected a pleasant and non-threatening image might have been a good idea.
Be sure to check out the AOMCI Don Peterson article to see photos of a Burtray!