In the bar I used to work in we used to give the change to customers on a tray to prompt the customer to give us a tip. So I always assume that's why they are being used.
Tipping, in various situations, is definitely a cultural thing which easily changes - even from the US to Europe. Guidebooks almost universally will tell you about what is expected. Different places handle different situations differently as well, such as tipping in a restaurant, to a bellhop, or to a taxi.
Similarly bargaining is diverse as well. You may not think of it, but in the US you bargain back and forth for big ticket items (cars, houses) but not little things. In many east Asian countries it is the opposite, you bargain with street salesmen but not for a motorcycle or car.
I cannot say I ever saw a tip jar at a sushi bar in Japan. Restaurants tend to adopt practices from the country they are in, even when the food is authentic. For example China does not have the concept of separate starters, main courses and desserts, but Chinese restaurants in the west often do.
A few places in Britain have put these jars out, mostly pubs in tourist areas and American codew shops. I've never put anything in them, since the previous container for spare change was a charity collection jar, usually for a local charity.
The charity jars are quite common in pubs, convenience shops and supermarkets.
A few years ago, I was almost forcibly prevented from leaving a Hawaiian burger joint in Nagano by a waitress who was concerned that I'd accidentally left some money on the table. I tried to explain that it was a tip, but they were quite unhappy to let us leave until we'd taken a couple of little candy canes - it was Christmas - from the display in their window...
Tipping is not a thing in Japan, generally. I've read that it can be considered faintly insulting, given the service culture - you're implying the recipient wouldn't have done their job properly unless you gave them extra money.