Generally, working from the bottom layer up:
Ruffle Sheet: Sits between the base and mattress components of an ensemble bed for decorative/ornamental purposes. (Optional.)
Electric blanket: sits on top of the mattress and is connected to an electrical cable which allows the bed to be pre-warmed. In the US, Electric Blankets are known as Electric Mattress Pads. (Non-optional in cold areas, especially if there are no other forms of heating available - eg hot-water bottles.)
Mattress protector: Flat (ie, non-fitted) but usually padded sheet with elastic added to corner edges. Goes over mattress to protect it and elastic slips under corners of mattress to keep it in place. (Optional.)
Bottom sheet: Can be a flat sheet, but is usually a 'fitted sheet'. Fitted sheets are elasticated in the corners to make it easier to a) make the bed and b) keep the sheet positioned correctly overnight.
Top sheet: Flat sheet. (Generally, bodies sleep between bottom and top sheets.)
Electric Overblanket: Largely a US phenomenon, these are similar to Electric Blankets/Mattress Pads except they are placed above the top sheet. In the US, they are called simply 'electric blankets'. This can cause some confusion.
[Blankets | Duvet/Doona/Comforter/Continental Quilt ]
Blankets: Generally thick (often wooly) rectangles that you add more of depending on how cold it is.
Duvets: (doonas in Australian) are bags with an insulating material (usually down/feathers, but also cotton and synthetics) inside. Usually (in contrast to blankets) only one duvet is worn on a bed. A duvet is usually wrapped in a duvet-cover which serves a similar purpose as pillow-cases do for pillows. In the US, the term is comforter, and confusion can arise as 'duvet' is sometimes used to refer to the cover/case specifically, unlike in Europe where it is the bag itself, or the bag+case.
Quilt: Top covering that serves a dual purpose as decoration and an extra blanket (depending on material, thickness etc). Not as commonly used with duvets as with blankets.
Quiltset isn't a single word (except perhaps in a marketing context), but quilt-set usually refers to a quilt / duvet cover that matches with pillowcases and possibly a ruffle sheet to create a coordinated look for the bedroom. The contents of the set (ie, whether you get two or four pillowcases, or whether a ruffle sheet is included) are dependent on the vendor (and price).
As snailplane has commented, for a number of reasons - different regions, different types of beds (eg, mattress protectors make no sense on a waterbed), marketing, etc - there is no hard and fast rule for all these names. However if you take this list while google-shopping, you should know what you want to order when you hit Amazon's checkout.