Weeeeeeeell... that's a long story. I can hit the high spots, though. A regulated mod has internal electronics. It takes power from the battery, does magical electron dances with it, and applies the outcome to the atomizer to make with the steam. A mechanical mod has no electronics. It's nothing more than a mechanical part that provides a structure to hold a battery, an atomizer, and a switch of some sort, and then directly connects the battery to the atomizer when you push the button. Most of them don't even have a "switch" per se. Just a spring loaded piece of conductor, usually copper, that closes the circuit when you push it and opens it when you let off.
Regulated mods, generally, operate in three modes. "Variable Voltage," abbreviated VV, the mod takes juice from the battery, runs it through a DC-DC voltage regulator, and apllies whatever voltage you set to the atty. A "variable wattage," abbreviated VW, mod measures the resistance (Ohms) of your atty, calculates what voltage is necessary to produce the wattage you set (V^2/I [resistance] = W, more about that later), and uses the same DC-DC voltage regulator to apply the required voltage to the atty to produce the set watts. The third mode is Temperature Control, abbreviated TC. This is a new thing, and they're still working out the bugs. The idea is simple: different juices react differently to different temps. So you figure out where the juice you're using makes good vape and doesn't burn, and control the temp of the coil to quickly get that hot, but no hotter. While the idea is simple, doing it is not. All metals change their resistance to conductivity with temperature, some more than others. TC mods require coils built of special wire (all can use nickel, some can do titanium) that is "high delta" or exhibits big changes with temp. The mod measures the resistance of the atty cold and stores it. Then as it fires , it measures the change in resistance, and from this calculates temp, applying more or less power to keep it in the sweet spot. Not all mods are restricted to one of these types. Most VV mods only do voltage, that's like an eGo spinner battery. Most VW mods can also operate in VV mode. Most TC mods also do VW; some do all three.
Ohms Law classifies the relation between potential (Volts, V), current (Amperes, Amps, A or I) and resistance (Ohms or R). Specifically, it takes 1 volt of potential to push 1 amp of electricity across 1 ohm of resistance. Electricty flowing through a conductor can be likened to fluid flowing through a pipe. Volts is pressure, how hard the pump is pushing. Amps is flow volume, like a 1/2" vs. 4" pipe. Resistance is anything impeding the flow, like sidewall friction or a constriction, or a sharp bend, all of which create turbulence. Watts is a measure of total power applied, or "work" in Newtonian physics, and is not limited to electricity, even though electricity is routinely described in those terms. Watts is the same thing as "horespower," just a different unit of measure (1 horespower = 745.7 watts). For electricity, watts = v*a = v^2/r = any other way you can algebraically express v, a and r by Ohms Law.
I first moved into mech mods and rebuildable attys because regulated mods were then limited to a total of 15 watts output and I wanted more power. With a mech, you have to do all those calculations yourself. The safety limit is how many amps can you safely draw out of the battery you're using. The voltage is fixed (within limits) by the battery voltage x how many batteries you put in series. A fully charged IMR cell delivers ~ 4.2 volts fully charged. A discharged one 3.2, but nobody goes that low because the vape gets weak below 3.5ish. The nominal voltage is 3.7. Stack 2 in series, 4.2 x 2 = 8.4 volts, and so forth. With a mech, the vape gets weaker with each puff, from full charge to depleted. Mech users live with that, and change batteries a lot. Since voltage is fixed, and amps limited by safety, about all you can change is the atty resistance by your coil builds. More watts? Lower ohms. Fewer watts? More ohms. A 20 amp battery, with a safety factor of 20%, can deliver 16 amps. At full charge, this can deliver 67 watts with a .26 Ohm coil. The same coil will draw 13.33 amps and deliver 46 watts when the battery is down to 3.5 volts. It's just math, and there are no exceptions to Ohms Law.
The cool thing about regulated mods is they can deliver ohm/watt combos a mech can't reach, because they can vary voltage. If you want to apply 35 watts to a 1.2 Ohm coil, you have to tickle it with 6.4v, and it will draw 5.4a. A mech mod can't do that. Now, I'm sure all this is as clear as mud, so keep asking questions.
