I've seen several shows where it looks like the bed has a quilted fitted cover for the mattress instead if a sheet and it coordinates with the cover. There doesn't appear to be a "top sheet" at all. I've never seen anything like that in the US and wondered what kind of bedding set that is (what it's called) and where to find them (I'm assuming online.) Does anyone know what I'm talking about? I can look up some examples if I have to, but it may take me a while to remember some of the shows I've seen them in.
Sometimes I think it looks like they're using a quilted mattress protector instead of a bottom sheet.  and then just a quilt.  I always wonder how it doesn't get all tangled in the night when they sleep and so why aren't the mattresses filthy.
I think you are talking about this kind of set:

http://item2.gmarket.co.kr/English/detailview/item...

If so, those are Northern European mattress pads, not to be confused with mattress toppers.  Mattress pads are thinner and attach with elastic bands diagonally at the corners of the mattress.  When you see them in cute sets they are part of a "collection" unlike a bedding or comforter set in the U.S.  

You can buy them quilted, heated, waterproof, stain resistant...etc.  In Europe, beds are made with a fitted sheet and comforter inside a duvet.  By adding a mattress pad above the fitted sheet, they can accomplish what a mattress protector does in the U.S. that is put underneath the fitted sheet.  Flat sheets are rarely used in Europe.

I noticed in Jealousy Incarnate that the t.v. station dorm rooms had beds fitted with the zippered mattress pads that cover the whole mattress and act as the fitted sheet and mattress protector in one.

If you search for quilted pads and quilted pad collections, you might find exactly what you are looking for online.  You'll also find a lot of the standard white toppers and protectors that are popular in the U.S.  Mattress pads in the U.S. tend to be used for crib bedding.

I don't watch enough k-dramas to have noticed, but I'm European and I've never seen the kind of colourful mattress pads as in Six link. It's interesting that there are so many different ways to make your bed depending on the country. I mean, just look at Japan, where you (traditionally) roll it out on the floor at night and in the morning you roll it up and put it away. :) Once, a friend from the U.S. visited me. She looked at her bed at night and said "what is this?!" Honestly, it took me a minute to understand the question because it had never occurred to me that a person could not have seen a duvet cover before. I just didn't know. She didn't even want to sleep with it, she wanted a single flat sheet and a blanket.

Flat sheets are perhaps rarely used in some parts of Europe like Six says, I have no idea, but they are very normal in Sweden (northern Europe). I've never been in a home where they didn't have them. When you buy a standard bed linen set you get a flat sheet, a duvet cover and two pillow sheets. So, in Sweden we make beds with a flat sheet and a blanket/comforter/duvet inside a duvet cover (it's called "bag sheet" in Swedish because it's like a "bag" to put the blanket or comforter in). But a mattress topper and/or a mattress protector/pad covered with a fitted sheet (often made of terry cloth, under the flat sheet) is also normal. I guess it depends on the type of mattress if you need a topper. :)
https://youtu.be/1OrUF8BfytQ

Here's an example from this episode of All About My Romance- ff to the 41:32 mark

And thanks for the suggested of looking up Quilted Pad Collections!
Check out DecoOne's stuff.  

http://www.decoone.com/

You're making me want a collection. '^.^
Thank you so much both of you! I'll have to translate the decorations one site, but it's got CUTE stuff!

And the aliexpress site looks good too! :)
Never in my life have I had a mattress pad, I have lived in Europe all my life xD 
You can find many on yes style :)
I will check it out - thank you @rosyprincess

I also have found this strange, especially in a country where so many do laundry by hand. The purpose of a mattress pad is to protect the mattress, which can’t be cleaned, from stains that might pass through the sheet. If you sleep directly on the mattress pad, a sheet beneath it serves no purpose.

The reason the sheet goes on top of the mattress pad is not  decorative but rather because it is easy to launder. Think about it:  whatever you use as the top layer between you and the mattress is going to absorb sweat and oil nightly and therefore will be the most frequently laundered. It is easy to launder and dry a sheet because of its light weight.

The mattress pad, which is bulky and takes longer to dry, is a pain to launder frequently. But protected by a sheet, a mattress pad usually doesn’t have to be washed more than every 3-4 weeks.