When searching for files in Thunar, you can only quick-search for files starting by the letters you type. This is fine, but using the Ctrl-F search shortcut should have a different behaviour, where you can search in the entire file name instead (showing only relevant files would be nice too). I've been looking in the code to find where this quick search box comes from, but grepping for search or key-press-event didn't seem to find anything relevant.
Sorry for the late reply! Take a try for pattern search "CTRL+S". Besides that, there is a bug which proposes to as well add pattern search functionality to the CTRL-F search, so I will close this bug as duplicate. *** This bug has been marked as a duplicate of bug 7514 ***