These are used everywhere in Japan, not just restaurants. At a convenience store, department store, the museum, train station, etc.

I've never seen them outside of a restaurant in the states.

But what is the point of using a movable tray in a shop or museum and so on, where employee has a cash or cash machine right next to it? And if the tray is just a place to put cash before other person takes it - such trays are used everywhere in the world.

I'm completely guessing here (never been to Japan), but my guess is that these are ubiquitous in Japan.

In the US the trays are common in restaurants, because the transaction is asynchronous. Anywhere else (gas station, grocery store, banks, shops) cash is handed directly.

I'm guessing someone can confirm on how widespread these things are in Japan.

Yes - every shop/restaurant/store/etc I went into used them -from low end to high end. They are ubiquitous in Japan.

It took a minute to get used to it as I'm used to handing money to people in the USA. I found some of the people I exchanged with would hand me the money back, hand-to-hand even though I used a tray.

It doesn't end there - business cards, receipts and numerous other things have a very specific way of being exchanged that were different to me. But all very cool and novel for me. Definitely worth reading up on some of the basic customs if you travel there. There was a high tolerance for foreigners not knowing how to do things the "proper way" but it's always good to at least learn a bit and try.

Yeah, it's common in German shops and take-away places, too.

I like the elevated trays in a lot of the German supermarkets and department stores that have the built-in scoop for holding change. Wish I could find a picture of it.

No that's not what I was thinking of. More of a small elevated shelf next to the customer where the cashier places the receipt and change.