Some general information, image and links:
The viola da gamba or "leg viol" saw its beginnings in 15th century Spain. Local guitarists (or as they were called "vihuelists") tried playing their instrument with a rabab bow (a bow for an instrument from North Africa), and the first viola da gamba was born.
The instrument retained everything from its original family: the frets, the tuning, and the playing position. It was held like a guitar, and was bowed vertically.
This instrument was quickly introduced into court circles in Naples, where the Italians started holding the instrument vertically and equipped the viol with a round bridge, essential to playing on one string at a time.
Soon afterwards instrument makers built the instruments in various sizes: treble, tenor, bass and double bass. The only rule for construction was the instrument builder's fantasy.
Description above from Jonathan Dunford's Viola da Gamba page
. Picture below from the Viola da Gamba Society of America
One striking difference between the two families is the addition of frets to the da Gamba.