I do love the technical term for them: deciduous teeth.
I have, among my keepsakes, a note of apology from a very young Jophiel Jr. who lost his baby tooth on the school playground and was deeply distraught. I told him that if he perhaps left a note explaining what had happened, he’d still get his coin. And so he did with all the charm a young child’s note to the tooth fairy could provide.
I think I like the note more than I’d have liked the tooth 
Either milk teeth or baby teeth would be understood here in Australia.
Hungarian - “tejfog”, literally “milk tooth.”
Scotland, milk teeth.
In Japan, 乳歯, Nyushi, which corresponds to Milk and Tooth for each character, so another dead on similarity.
Here they don’t have a tooth fairy though. Instead a child throws the tooth UP as high as they can if it’s from the lower jaw, to encourage strong, straight growth in the next tooth, and if it’s from the upper jaw, they throw it DOWN from a window as hard as they can.
Chinese: 乳齒 (almost the same as the Japanese kanji, same meaning: milk tooth).
Dutch:
Melk tanden=Milk teeth
The slang term in the East Midlands is teggies or tegs. Technically refers to teeth in general, but in usage mainly refers to children’s teeth.
In Italy a mouse comes for the teeth, and they are called Dente di Latte, or milk teeth!
In South Africa a mouse comes, and you leave your tooth in a shoe, or slipper under your bed.
There is a wonderful book called “Throw Your Tooth From The Roof” which looks at what children around the world do with their fallen teeth.
Since no one has responded about why they are called milk teeth, I’ll give my guess: there was some idea that the kid got these teeth because he was fed milk from his mother. In fact, it wouldn’t surprise me if there was at one time a tradition of stopping breast feeding once one’s milk teeth came in.
That’s all I have, since the only other thing I found out about the term is that, in English, it dates from 1727
One of my favorite viral videos is of a little girl who had tried to pull a fast one on the Tooth Fairy (mom was filming the whole thing). The lass had lost a tooth, but had decided to keep it for later, in case she needed money at a later date. Instead, she wadded up some paper in a more-or-less tooth-shaped blob and proudly told her mom that she would leave this under the pillow instead of her tooth! Profit! Cut to the next morning- Little girl is visibly angry. Mom asks her, “Did the Tooth Fairy leave you any money?” “No!” says the little girl. “She left me a ticket!” She then shows the camera a note from the Tooth Fairy that says “This is NOT a tooth!”
Zęby mleczne in Polish. Also corresponds literally to “milk teeth.”
I don’t get the chance to be a grammar nazi for the Dutch language very often anymore, so I’m going to enjoy this! Melktanden is one word!
incidentally, it’s mléčné zuby in Czech. Means ‘milk teeth’
Hebrew: שיניי חלב shinei chalav. “Milk teeth”, of course.