I can't speak to the VB line of products, but the Inhalater is a different scenario since it draws significantly less power to heat the element than the Solo does. My 004 drew 1.2A at 4 volts when the heater was connected, which is about .4C. I think this is because the polyimide has such a high thermal transfer rate when compared to the metal or ceramic in the Solo.
A C is a measurement of output or input power relative to the capacity of the battery in use. Most batteries are marketed by their total capacity (Amp-Hours), but a C refers to how much power it is putting out (or taking in) at any given time. So to use the Solo's pack as an example, which is 2200mAh @ ~7.4v; 1C of power in this case would mean that one C is 2200milliamperes of current. The one in the INH is a 2800 cell, so 1C for that battery would be 2800mA, or 2.8 amps. Charge currents are also measured in C's, and it's generally recommended to charge a battery at or below .5C, or half of it's total capacity. These stack too, so if you are charging a battery at .5C while discharging it at 1C, that battery is under 1.5C's worth of stress.
ICR batteries (the kind used in both these and most other portable vapes) don't like being used past around 1C. With the Inhalater, this never happened because heating the element used around 0.4C, leaving enough room for a respectable charge current to be applied at the same time. And it would never charge the battery enough that you could run it for long periods of time, your battery would slowly loose capacity if you just constantly ran it on. So the battery was never ran past the 1C level. But I'm worried that if the Solo uses 2.2A of current in operation, and it's being charged at .3C, that's at least 1.3C of stress on that battery and that is not good.