There is often confusion between classification of the chitarrone, theorbo and archlute. The definitive discussion was written by Robert Spencer, and additional useful comments by Nigel North are available in his 1987 book Continuo Playing on the Lute, Archlute and Theorbo (out of print, but copies are generally available). Both lute and archlute are differentiated from the "traditional" lute in that they have a neck extension and additional tuning box to provide strong bass diapasons (or bourdons); in essence, both are a kind of archlute. 

For all practical purposes, the chitarrone and theorbo are one and the same. They probably evolved from bass lutes that were tuned up, but because of their long string lengths the top one or two courses simply couldn't be brought up to pitch, so they were dropped an octave, forming was is referred to a re-entrant tuning. Furthermore, the theorbo typically was tuned up one whole tone, which changes the keys it favors playing in. So, in short the primary differences between an archlute and theorbo is that the archlute maintains the traditional vieil ton of the Renaissance lute, whereas the theorbo is tuned up a note and the top one or two strings are tuned down an octave.