XYplorer Beta Club

With no boxes checked a search for "bg.jpg" is the same as searching for "*bg.jpg". Is this the intended search pattern or something that has appeared as a result of the fuzzy search? I've not noticed it before and it's not the same as having fuzzy search selected.

Yes, this is intended. Actually, searching "bg.jpg" with no boxes checked is the same as searching for "*bg.jpg*" (wild cards on both sides). This is mimicking the behavior of Windows' native File Find, and it was always my policy to meet the expectations of the masses.
Your question also serves to explain the purpose of the "Exact Match" check box: if checked only "bg.jpg" will match a search for "bg.jpg" (unless Fuzzy is checked, too).
The exact functionality is like this: IF "Exact Match" is unchecked AND "Fuzzy" is unchecked AND no wildcards are present in the search pattern THEN * is internally added to both ends of the pattern resp. of each pattern in a Boolean Expression.