_The plectrum banjo is the same scale length as a regular 5-string (not a long-neck). It's not a 5-string with the 5th string removed, but a legitimate banjo in its own right. It's often tuned CGBD or DGBD and sometimes DGBE (Chicago tuning). Eddie Condon, although some say he played a tenor guitar, actually played a plectrum guitar, tuned, I believe in Chicago tuning, as did Tiny Grimes.
_The tenor banjo has a shorter scale length and the standard tuning is CGDA. Irish players use what's called "Irish tuning", the one pdq mentioned above, which is GDAE, an octave below the mandolin or violin, very handy for playing fiddle tunes. I've seen tenor banjos tuned Chicago-style, DGBE and ukulele-style GCEA (or gCEA) or standard CGDA, up two frets to DAEB.
_A shorter scale tenor banjo is called a "Tango banjo". It's a couple of frets shorter than a standard tenor and is favoured by Irish players.