Yep, Tile I believe is the only third party service that exists. All other trackers either plug into "Apple Find My" or "Android Find My Device" network. There's finally starting to be a few devices that can do both, but they're rare, so make sure you get the right one when buying. But they take 10s to setup and it's very smooth.

Any names or recs on the ones that can do both? Can they do both simultaneously?

Samsung trackers also use their own network.

Tiles are about the same price as AirTags (at least they were last time I bought some)