> What is it that these apps offer that the default Google podcast doesn't?

For one, donating directly to the podcaster herself instead of to Spotify/Google/Anchor/Apple or whoever else runs the app.

> Does it give better discovery options?

Sort of, yes. Let me explain: All podcasting apps rely on the Apple podcast index. [1] One of the very early podcasters, Adam Curry, was worried about this index being run by Apple, who may or may not one day decide to censor the index or ask money for it. So he set up his own [2].

[1] http://adam.curry.com/html/PODFATHER-g6c2RMsVnxgTdZ2DgHlVfMv...

[2] https://podcastindex.org/