I believe you are talking about a tenor guitar. They were popular in the 50's and early 60's (Kingston Trio).
According to Wikipedia:
Tenor guitars are normally tuned in fifths (usually C3 G3 D4 A4, similar to the tenor banjo, mandola, or the viola) although other tunings are also common, such as "guitar tuning", "Chicago tuning," or baritone ukulele tuning (D3 G3 B3 E4).
Except for the "fifths" tuning intervals, it is basically the same thing as a baritone ukulele, although tenor guitar may be slightly bigger than a typical baritone uke. All the chord shapes will be different because of the tuning, but you would fit right in with the mandolin / tenor banjo crowd.
