What country are you in?

There are a bunch of different protocols used to exchange scheduled and live transit information out there. And there are also a lot of different companies actually operating the vehicles (Transport Authorities). Sometimes several within one large city. But even if they have different systems underneath often they expose one of the popular protocols. Often there are even rules/law about certain protocols that you HAVE to support.

In USA that is mostly GTFS and GFTS-RT. I dod not think its a law but something about what you have to do to get funds maybe? I'm in Europe so my memory is foggy.

In EU I believe its NeTEx and SIRI. And every member nation needs a national hub where all transport authorities shares its data openly.

GTFS + GTFS-RT is very popular among consumer apps since its both pretty simple and pull-based. Static data is in CSV-files in a ZIP-file and the realtime data comes via Protobuf. If you check sources on the page this post is about you will se many GTFS sources. Ofc even transit systems built for the european standards can expose GTFS via a translation layer to support a broader range of consumers easily.

When it comes to signs at bus-stops there are those that are fed with this kind of data and can show both timetable data and realtime data based on the vehicles position. Here those signs are everywhere (Sweden) and I know there are plenty in the rest of Europe aswell. Outside of that I don't know if they are used as much.