The plectrum banjo does NOT predate the five-string, having been introduced for the banjo-band craze of the late 1800s-early 1900s. Joe Hickerson once showed me an ad from, I think, 1909, for a five-string banjo with a special hook which you slipped the fifth string under (also slipping it to the side of the bridge) so as to drop it out of the plane of the other strings for plectrum use. The plectrum banjo is typically tuned like the "classical" banjo, CGBD (low to high), and is a melody instrument in the classic banjo band.
The tenor banjo, developed around 1910-15 (as a commercially-made instrument), has 17 or 19 (not 20) frets, and is tuned like a cello (CGDA). It is primarily a chordal instrument (and I seem to remember that Eddy Peabody played lots of chord-melody, so my guess is he played a tenor). Use of it by Irish musicians for melody is an example of the "dog walking on hind legs" syndrome (it's not that he does it well, but that he does it at all) -- the plectrum is actually a much better melody instrument than the tenor, but the tenor is what gets used. (Probably a supply-and-demand thing there; tenors are a dime a dozen and plectrums are pretty rare).
The five-string banjo, which passed into white use about 1830-40, was one of many kinds of banjo-like instruments found among African slaves and freed blacks in the 1750-1850 period. Some evidence exists that the fifth string that Joel Sweeney supposedly "added" was, in fact, the low (4th) string, and the thumb string -- chanter -- was already in wide use among African banjo players. The non-use of the fifth string in some musics, like in Australia, probably relates to the prevalence of the 6/8 and 9/8 celtic-based tune in those areas. It's hard to play jigs on a five-string, especially if one uses the down-picking "Clawhammer" style of southern US players. I hold, in fact, that that difficulty is one reason that southern fiddle players don't have very many jigs, strathspeys, or hornpipes -- played in the original time signatures -- in their repertoires. Accompaniment by the banjo, the most common fiddle accompaniment instrument in the south, was difficult, so the tunes got dropped or turned into reels.
Anyway, that's what I know about the various banjos (the guitar banjo and banjo-mandolin, which have been mentioned, were a part of that late-19th-Century period of experimentation with banjo-like instruments I cited earlier). I have a bunch of the things (several fives, one tenor -- but no plectrums, and no electrics -- a six and an eight, and a couple of banjo-ukes), but tend toward guitar and mandolin these days. Haven't found any in the trash, either, nor bought any on eBay (actually, I did, but it was for my sister in Iowa).
There, have I covered all the significant sub-threads in this one?