Not necessarily? As far as I know they come from the same WebKit source. But the bridge between WebKit and the OS is of course specific to each system. WebRTC is still experimental in webkitgtk while caniuse says Safari supported it back in 2017.
I remember encountering one bug with Final Form that triggered rarely in Safari, 100% in Webkitgtk, and never in Chromium.
Here's the developer of Tauri saying it's hard to recommend webkitgtk / Linux support:
> So if you need good linux support now/soon i can't 100% recommend tauri (for Linux) as of now. (I used to be more "forgiving" but with webkitgtk getting worse/more unstable each release i changed my mind)