There is not one blanket statement that covers all the different types of electronic cigarettes, so we'll run by a few of the basics. First up, we have what is commonly called a "Cig-A-Like" due to the fact they resemble a cigarette. There are dozens of brands, but the most well known are produced by tobacco companies. In general, they're expensive to maintain and overall ineffective due to their minimal vapor production and limited selection of flavors.
From here on are more powerful devices, often referred to as "Mods", though even that term is separated into "Regulated Mods" and "Unregulated Mods" which can technically be broken down even further - but we won't go there. Both are essentially a battery pack for the atomizer (the part of the device which creates the vapor). This example here is a regulated mod. It uses special batteries that give it tons of power, magnitudes more than the vape pens, but has protections that prevent the battery from overheating or shorting. They come in various shapes and sizes, and are sometimes referred to as "Variable Wattage Devices" as their power output can be adjusted. They can be anywhere from a 15 Watt device to a 260 Watt behemoth. The options allow for the vaper to pick and choose what works for them.
This is what is referred to as a "Rebuild-able Atomizer" where the vaper uses a special wire (the most common is kanthal wire) to create a coil which is then wicked with cotton, rayon, or silica. The device heats the liquid soaked wicking material and the vaper then inhales the vaporized liquid. There are two types. The one pictured is a standard rebuild-able, but they also have a secondary type that combines a tank with a rebuild-able deck so the vaper does not have to constantly drip juice onto the wicking material. Now they are not for beginners, as there is more to them than simply sticking a coil on them and firing away. Consult your local brick and mortar vape shop for more information in regards to rebuild-able atomizers.
This is what is commonly referred to as an "eGo Tank", and is the most basic of atomizers. They may or may not have replaceable coils (this kind are pre-made, so no need for the vaper to build them). They typically have low air flow, but are very inexpensive as far as atomizers go. You may spend $3 to $5 on one of these, whereas you could easily spend $35 or more on the rebuild-able type to the left. They are most commonly used by beginner vapers.
For the sake of keeping it simple, I have also provided links here to what these ingredients are. This said, if you choose to import your juice from overseas or order from a company that sells you say - 120ml of juice for $5 - you're taking a chance that the ingredients are not food grade. Rule of thumb. If it sounds too good to be true, it probably is! If you have any questions, feel free to ask your local brick and mortar vape shop!
This is extremely exaggerated, and is also based on the assumption that e-liquid is pure nicotine and that the body absorbs 100% of nicotine (it doesn't, it's more like 30% actually absorbed). A bottle of e-liquid has a nicotine milligram count. A 3mg bottle has 3mg of nicotine per milliliter (which is way more than a drop), and a 24mg bottle has 24mg of nicotine per milliliter. 24mg is the highest you can buy in most places.
Here is the lethal dose information on Nicotine:
"The fatal human dose has been estimated to be about 50 to 60 mg [Lazutka et al. 1969]. [Note: An oral dose of 50 to 60 mg/kg is equivalent to a 70-kg worker being exposed to about 30 to 40 mg/m3 for 30 minutes, assuming a breathing rate of 50 liters per minute and 100% absorption.]"
So, basically, it's impossible for standard liquid dropped on the skin to kill you. No one is going to just leave copious amounts of e-liquid on their body without wiping it off.
That said, people who DIY their juice, have access to 100mg per milliliter nicotine concentrate. This stuff CAN BE deadly, and should only be handled by those familiar with the dangers of pure nicotine concentrate. Gloves, goggles, and a syringe. The odds of this stuff laying around somewhere kids can get it is extremely slim. Your kid is more likely to be poisoned by a Tide laundry packet than 100mg/ml nicotine concentrate.