Please explain car seats to me!

Please, in the most basic terms. I know nothing.

Here's the context: I live in a big Asian city; we don't own a car and mostly travel by getting taxis (ride-hailing app, Asian version of Uber - more affordable). I'm pregnant with first baby and have no idea what to do about car seats?!

I'm from the UK and everyone I know has their own car so they just have their permanent car seat that stays in the car. Or I've read about having a base attached, and you clip a seat on and off.

So can you get carseats that can be moved from car to car, without the need to have an attached base to the seat? What are these called? Can I attach them to a pram (stroller)? We're thinking about getting the Yoyo pram as we really need portability in a big city. Please walk me through it.

If I google it, it says you can just have a pram upright in the taxi but this is talking about black-cab-style taxis with wheelchair space.

We can't be the only people in this situation surely. I just can't find the right answer or they assume too much knowledge and I get lost. Please help!