Each client has its own way of sending zaps. This is not a technical issue, but more a regulatory or App Store issue.

Primal managed to register as a financial services company, which allows them to include a built in wallet for their Android and iPhone apps, but not their desktop client.

Damus on the other hand is simply an app and therefore cannot include or directly link to a wallet. A hack solved this and so most Damus users run https://zap.army/ which allows them to zap notes via their favourite wallet.

There is no inherent connection between the wallet you send zaps from and the app you use for using the NOSTR protocol.

My profile header has a link to my site with an article explaining NOSTR if you want a deeper understanding.