Watts is watts, and watt-hours is watt-hours. Your battery is rated in milliamp-hours, and that-- barring mislabeling, false advertising, and deterioration of capacity through usage/damage-- is what it holds. An "Amp-hour" is that amount of capacity that will flow a current of the specified amount (6 amps, 2200 milliamps, whatever) for one hour at the battery voltage. Watts are a measure of "power" or "work" in the physics terms. Amps are a measure of the amount of current flowing at any given time. As simply as I can, mAh tells you what current level the batt's capacity will deliver for 1 hour; while mWh is a direct reference to the batt capacity itself. The capacity rating does not necessarily indicate the batt's ability to transfer power; that's what the "C" rating is for. Thus, a 1200mAh battery will deliver 1.2A for one hour before it is discharged. Or it will deliver .12A (120mA) for ten hours. Or it will deliver 12A for 6 minutes (if it's C rating is high enough and it doesn't blow up.) Milliwatthours work the exact same way, it's just a different unit of measure, measuring a different thing. The exact calculation of how many Wh a battery holds would make Einstein stagger across the room for an Advil; it's pretty hairy math because actual delivered voltage changes over the charge state. Watts are equal to amps times volts. A rough-and-ready guide is nominal batt voltage times mAh rating; example: 1000 mAh batt at 3.7V is about 3700 mWh or 3.7 Wh or .0037 kWh. It is important to note the math doesn't care about the values: a 1V, 1A current, and a .1V, 10A current, and a 10V, .1A current all use 1W/time unit the circuit is energized.
In practical terms, there are other considerations. For example, if you're a chain vaper using hi-watt setup, and you're working close to the battery's effective maximum C, the batt will heat up. Elevated temps derate the batt's ability to supply power. You're not using a meter to determine this stuff, you're using your mouth to tell you the quality of the vape; an imprecise metric at best
This is to say, the rated mWh are still in the battery, but you can't get them *out* of the battery fast enough for your mouth to tell you "good vape" under hi temp conditions. For your purposes, then, the batt is "flat", even though it's still got juice, and would cheerfully deliver it if you let it cool down first.
The thing about VW mods-- why they work so well-- is by controlling the wattage used, they always apply the same amount of total power to the coil for however long you have the fire button pressed, thereby giving you a very consistent vape. Within limits, they don't care about the atty resistance; they just apply the right current at the appropriate voltage to burn X watts-- wherever you set it-- for as long as you hold the button down. State of the art being what it is, there are some practial considerations. The board can't deliver more power than the batt can provide, or so much current it melts. There's usually a limit to the ability of the board to measure the atty resistance; if your coil falls outside those limits, the board can't calculate A x V to give you the W you want. A TC mod won't exceed the specified temp, even if this means delivering less wattage to the atty. A mod with a pre-heat function heats the coil to just-below-vapor-temp for your juice so it fires quickly, but this uses batt power when you are not vaping. In general, though, and all else being equal, a thinner wire/fewer wraps coil vs, a thicker wire/more wraps coil both totalling the same ohms shouldn't make a practical difference in battery life. The thinner coil makes vapor more quickly, true, but usually less than a second's difference, and then only on the first puff from a cold start. There are 3600 watt-seconds in a watt-hour; and you're likely to want to charge/swap batts long before the batt is dead flat. YMMV, if you have a precisely calibrated vape-mouth; but prob not so much in practice.
!) I also notice the sudden drop-off of flavor/vapor when I run out of juice, long before I experience any dry or burnt hits. (Thank you, Rayon and JeremyR!) If we learn how to build them correctly and utilize our devices within their intended parameters, TC becomes less of a necessity and more of a toy.
