The infinity bath is rather unusual and is an infinity bath. Those who have used them will know this. There is no overflow the water can be continually run and drops over the edge of the bath continually into a decking area in surround all sides of the bath. It is in some ways like an infinity swimming pool but far smaller.
The water pour is from a waterfall tap head and is supplemented by a shower head (water flow switchable between the 2 modes like many hotel or cheap home bath shower combos).
For those who haven't yet tried these and who are eligible I really recommend it if you have a fair bit of spare time.
There are a couple of seats in the bath area too and IIRC a bidet as in the CCR toilets.
I think this picture illustrates best:-
As you can see from that image the tap is very like the taps on the hand basins in the main CCR cabanas but with an added shower head.