Practically everywhere where they exist, they differ from the american ones in one crucial detail: all four wheels swivel. Which means maneuvering is completely different - you can push them sideways, turn them on a dime, and when they're full it's a tad harder to run them straight - they'd go where the slope drives them, to the rain drain.
They exist only in larger supermarkets, mostly chains like Lidl (german), Zira (unknown), Tempo (ditto), Maxi (a branch of Food Lion i.e. Deleuse, though they don't say it anywhere but have the same logo), Idea (owner unknown, allegedly not local because it would spell Ideja then), Svetofor, Mere (russian). Roda (slovenian with fresh croatian owner), Gomex, Persu (both local of Vojvodina) run the mix - there are carts, and there are baskets, you can use either.
They are generally in better shape than what I pushed in Kroger, K-mart or Walmart. There are also some semi-carts, a combination of a shopping basket and a travel bag - two wheels, telescoping handle. All plastic (except the telescope) and sometimes in bad shape. Actually, so far the only place with bad carts, including these semis, is Roda.
To return the carts, you're expected to return them either to a gathering place near the entrance, or into the pen. Lidl uses a token lock - each cart locks into the next, so you insert a token (which they give out for free) or a coin of 5 RSD, which you get back when you lock the cart into the next one in the pen.
The carts being a relatively recent thing - back in the eighties perhaps two shops had them - they still mostly aren't worn out. By 2023, however, I've started finding carts with the same faults as those of Kroger or Walmart were prone to have: wheels with uneven padding, swivel axles bent so the cart pulls to one side. Somehow those bent axles are restricted to the two russian shops, even though they are the latest - opened in 2023.