As far as I know, they both communicate wireless with the ‘Tado Internet Bridge’, for sure the wired version does (I have one), so, why shouldn’t the wireless one do the same?
If you mean the Tado Bridge X, you’re right, except that for the wired version you need a separate ‘Bridge X’, and for the wireless version you don’t, in that case the ‘Wireless receiver X’ has a ‘Bridge X’ on board. An other option is to use Homey (2023) as a border router, or any other Thread border router.