Hi Springheeled. The subject can be quite confusing, as there's loads of options out there. There are certain things they all have in common - a battery part, an atomiser with a metal coil (powered by the battery) to heat & vaporise the liquid, and a container for the liquid.
To summarise the main different types, you have:
Disposables. These are single use e-cigs, with all 3 main components in one sealed unit. Definitely the most expensive way to vape as everything is thrown away after one use, and they tend to be very limited in the flavours etc. available. Tend to be used for emergencies e.g. a smoker who is somewhere they can't smoke, or a vaper whose kit isn't working while they are out.
Cig-a-likes. These are the e-cigs that are roughly the same size and shape as tobacco cigarettes, and what until recently almost everyone thought of when you talked about e-cigs.. The battery is re-chargeable, and the user buys disposable cartridges or cartomisers which contain the atomiser/coil unit and the liquid. These are a bit cheaper than disposables as you only throw away the cartridge when it's used up. Though the range is better than that for disposables, it's still quite limited on flavours.
For both disposables and cig-a-likes the vaping experience is OK-ish but not great, and many of the companies who just produce these get the carts and liquid made as cheaply as possible which can affect the quality.
Battery and tank systems. These e-cigs have a larger rechargeable battery and a separate re-fillable tank unit (also known as a clearmiser or clearo) which also contains the atomiser. The user buys the liquid separately and refills the tank as required, and often the atomiser part is replaceable too. Buying the liquids separately is significantly cheaper than buying replaceable carts, and as long as you use a recommended and reputable brand the quality should be fine.
The vaping experience is much better than either of the other types and there's a massive range of flavours and strengths available. There's various sizes, shapes and types of batteries and tanks out there and it can be really confusing to someone new to the subject.