fredmrichard is correct - the Android Gospel Library search is "exact phrase" whereas the LDS.org search appears to be a weighted "any words" search (though it appears to have been updated recently to support phrase searches (by putting the phrase in quotes)). Finally, based on the help videos linked below, the iOS (Apple Gospel Library) searches either as "all words" or "any words" (couldn't tell which from the video, but definitely not "exact phrase".
http://gospellibrarytraining.blogspot.c ... me-of.html
...start at about 3:30 and look at the search results when they finally come up - it's clearly not exact phrase. (NOTE: This does look like it might be the previous version, so maybe they changed how it works, but if so, they should go back...)
I too vote for the Android Gospel Library to be updated to a weighted "all words" search - remembering exact phrases is almost impossible for most mortals, and it's just a LIKE query in SQL with some % wildcards in it... I would also love to see the search results grouped by author rather than or in addition to by book - e.g. I know Holland gave a conference talk with "peaceable things" in it, but I'm not sure when - I have to dig through boatloads of general conference results to find it because a) the search is currently exact phrase and b) it only searches the text, not the metadata, so including the author's name in the search criteria doesn't help me.
Liz