Hi Gene,
The world of photo metadata is fraught with rumor and innuendo. There is however. the IPTC who have a tireless sub-committee that worked out an published standards for such things. Unfortunately the photo software developers, photo sharing sites and camera manufacturers have tended be how shall I say "Relaxed" when implementing them.
So here are the definitions of each in the latest 2010 Photo Metadata specification on the
IPTC Photo Metadata site.
Title:  A shorthand reference for the item (or digital image). Title provides a short human readable name which can be a text and/or numeric reference. It is not the same as Headline.
Headline:  A brief synopsis of the caption. Headline is not the same as Title.
Description (Caption): A textual description, including captions, of the item's content, particularly used where the object is not text.
This wording has been around since the 2007 document so Adobe has had plenty of time to adjust. So while Adobe claims to IPTC compliant they selective with which parts that they choose to support. Of particular note they support Title in the Filter Bar and Smart Collections but not Headline. They also make it rather difficult to use Headline, you can only find it in the IPTC Metadata preset all the rest use Title instead and they give you no method to make your own presets.
Out in the web different sites will use one or the other or both. Flickr for example will use either as the text displayed with your images. If both are present it will default to one but I don't remember which.
Right now I just use Headline because that to me that is where one should store the quick description of the image I want displayed and leave the Title field blank. To work around the built in limitations of Lightroom I use Jeffery Friedl's
Metadata-Viewer Preset Editor to make my own metadata presets and the Parse and Audit function of John Beardsworth,s
Search Replace Transfer plug-in that gives you direct access to these and other fields in the Filter Bar and in Smart collections.
I hope that this at least lays out the landscape and you can make an informed decision based you your needs.
-louie