Are the sizes of mattress we find here in the US (king, queen, twin, etc.) standardized across other countries? If they are, what are they called in other European languages?
For reference, the Wikipedia Bed Size page states common US sizes are:
Twin (39in x 75in = 99cm x 191cm)
Full/Double (54in x 75in = 137cm x 191cm)
Queen (60in x 80 in = 152cm x 203cm)
King (76in x 80 in = 193cm x 203cm)
Not exactly Europe, but in Colombia the mattress sizes are close, but not exact size matches.
Some locally produced lines advertise by sizes in cm. (90x190, 100x190, 120x190, 130x190, 140x190, 160x190, 180x190, 200x200).
Some other lines use Spanish words Sencillo 100x190, Doble 140x190, Queen 160x190, King 200x200 (Single, Double, Queen, King).
The Wiki page has terminology and sizes in some other European countries/languages.
Yes and no. Mostly no. Some countries and groups of countries have similar sizes but lots use the same terms for slightly different types. Wikipedia has a great article on bed sizes that I can’t work out how to link to on my phone - helped a lot with my recent emigration to a country which seems to use its own sizing all together!
French King and Queen sizes are about 9 inches shorter because they don’t need the extra room 
A tip: you can go to a page on Wikipedia, like Bed, and pick a language on the left. If you can muddle your way around, many have sections on sizes. Interestingly, bed size is only English, but gives some international information.
It’s not a matter of language, but of country.
In Spain the standard sizes are referenced by length (older beds were shorter than current ones, for a while people would ask specifically for cama larga, “long bed” and now they may need to specify cama corta, “short bed”) and width: de matrimonio (“marriage bed”, similar to a Queen’s), de 80 or de 90 (cm).
A couple of local mattress makers (webs in Spanish but you can access their catalogs and get an idea of what the sizes are):
Flex.
Pikolín.
As far as I can see, there is no ‘standard’ at all. These terms (King, Queen, etc) can mean anything the manufacturers want them to mean. They are no better than ‘Economy size’, ‘family size’, or any other description an advertising company can come up with to make one product look better value than another.
Looking at Ikea and a large Norwegian furniture store chain every adult bed is 200 cm long and come in various widths between 75 cm and 200. Each model comes in some subset of these widths: 75, 80, 90, 120, 140, 160, 180, 200.
Information for hotel rooms occasionally use approximate US terms for touristy purposes.
They differ between the Netherlands and the UK, I know that. There are different words and intermediate sizes (eg in the Netherlands you have the “twijfelaar”, “undecided”, can be anything from 1.20m to 1.40m).
Also, in the Netherlands the standard length has been adjusted to 2.20m, so that’s another difference. It also depends hugely on how old the bed is, because a standard single used to be 70cm, and now it’s 90cm. In turn that means a standard double used to be 1.40m but is now 1.80m. If you ask a dodgy old hotel if they have “double beds” they might reply that they have, and you might find them tiny.
I don’t know exactly how to convert, but I have been going between countries with my sheets for some time, and I feel that nothing ever fits properly.
I think IKEA always has different sizes as well. They certainly have pillowcases that only fit their pillows. So don’t trust the Swedes either! 
They differ between the Netherlands and the UK, I know that. There are different words and intermediate sizes (eg in the Netherlands you have the “twijfelaar”, “undecided”, can be anything from 1.20m to 1.40m).
Also, in the Netherlands the standard length has been adjusted to 2.20m, so that’s another difference. It also depends hugely on how old the bed is, because a standard single used to be 70cm, and now it’s 90cm. In turn that means a standard double used to be 1.40m but is now 1.80m. If you ask a dodgy old hotel if they have “double beds” they might reply that they have, and you might find them tiny.
I don’t know exactly how to convert, but I have been going between countries with my sheets for some time, and I feel that nothing ever fits properly.
I think IKEA always has different sizes as well. They certainly have pillowcases that only fit their pillows. So don’t trust the Swedes either!
Thank you for the update. It looks like like they are only very slightly smaller than their U.S. counterparts.
UK bed names and sizes are also different from the US. We don’t have a Queen size I don’t think, unless there’s been some rebranding going on that I’m not aware of. I often see it on hotel websites and have no clue what it means.
We have single, small double, double, King and Superking, from memory.
Note: Bumped by a spammer, whose post has been removed.