The tenor guitar was a transition instrument for banjo players to be able to double on guitar, thus not losing their gigs or status. It was originally tuned CGDA, the same as viola, tenor banjo, mandola and mandocello (an octave lower).
These days some people restring and retune tenor and plectrum banjos and guitars to the same as the top four strings of a guitar, DGBE, thus allowing the ability to double on tenor banjo and tenor guitar without having to learn a new tuning. The Kingston Trio was the main reason for the popularity of the tenor guitar and this tuning in the early 60s. Some folks restring and tune tenor guitars to an octave below the mandolin, GDAE. A number of instrument manufacturers are now making good quality guitar-banjos, banjitars, etc.
Since I already play other fifth tuned instruments such as mandolin, fiddle, tenor banjo, etc, I mostly use the original tenor guitar tuning, CGDA, which is a versatile tuning for many styles, including swing. I've also tried various open tunings on it, including CGDG, DGDG and CGCG.