It's all about the volume of fuel relative to the size of the cook chamber. All things being equal, a small properly combusting fire (i.e. as evidenced by "TBS") will generate a certain amount of heat. A larger fire (more fuel) combusting with the same efficiency in the same smoker will generate more heat. The exhaust gas' visual characteristics (i.e. the "TBS") are the same, but the temps are higher. Billowing white smoke is simply a visual cue that the fire is smouldering, i.e. not combusting properly and releasing water vapor into the gas stream. This environment is perfect for the formation of creosote on the inside of the pit -- and on your proteins.