Digital electronics are circuits where different voltage levels are separated into discrete steps, usually on and off (0 or 1). The important part is that one range of voltages is lumped together into one value, and other ranges of values are lumped together into other values. That's where the "digits" part of "digital" comes from. So, for example, if you had a circuit where everything between 0V and .25V was lumped together to mean 0, everything over .25 but less than .5V would mean 1, everything over .5V but less than .75V meant 2, and everything over .75V meant 3, then you'd have a digital circuit.
Analog circuits are where the value of the voltage can vary continuously over a given range. It could be 3.14159265... or 3.2, or 2.7182814... or 2.75, or whatever value. Each of the infinite possible values is different from the other possible values. When you turn the volume knob, and the music gets louder and louder steadily, that's an analog circuit. When you press the volume up button and the volume gets a fixed step louder for each button press, that's a digital circuit.
So, what does any of this have to do with cigarette smoking? Attaching a coil to a battery, where the voltage of the battery and the resistance of the coil causes the coil to heat up, and deliver the heat to a wick is not an example of what I would call a digital circuit. The voltage is continuously variable in the circuit and affects the output. There are no "digits" or ranges of values with a fixed meaning, so it is not digital. If I had to call it something, I would call it analog. On the other hand, if you have a computer controlled regulated device, then you might actually have something you could call "digital." Either way, cigarette smoking has absolutely nothing to do with analog circuits, and the only reason that calling cigarettes "analog" even vaguely makes sense, is to contrast it with so-called "digital" smoking. But, it's not digital, and it's not smoking, so the whole thing is just plain silly in my opinion, and makes no sense at all.
I think calling them stinkies could hurt someone's feelings, but I did happen to walk past one of my students in class yesterday, and it was OBVIOUS that he was a smoker (I didn't actually know he was a smoker until then). So, there you go.
You may find this difficult to believe, but it's OK with me if you call it anything you want, as long as I understand what you're talking about

But, when I write, I usually don't use the terms "analog," "digital," or "stinkies." I usually refer to "cigarettes," "atomizers," "batteries," "mods," and so on. Some of these terms are pretty arguable as well (like most mods now-a-days aren't really mods, in the original sense). I suppose I should say vaporizers instead of atomizers, or something, but atty is short and easy to type.