Third party browsers on iOS use the same web engine as Safari (WebKit) but critically, do not wrap Safari itself. In principle third party iOS browsers are no more wrappers of Safari than fully independent desktop Linux browsers built with WebKit like Epiphany/GNOME Web and Midori.

The various Chromium based browsers are much closer to being Chrome wrappers than, say, Firefox for iOS is a Safari wrapper because the latter has totally unique code for UI, interactions, password management, etc whereas the former is literally just Chromium with a few surface level changes.

Apple could stand to allow third party web engines either way (perhaps with strict performance requirements, to not destroy user batteries), but I think the distinction matters.