I was there last July. The Zoo closes at 18:00 and the Night Safari starts about 19:30 so there's no overlap.
I spent the day at the zoo, but left early - around 16:00 - to include the River Safari, which I rushed through. Although it closes at 19:00 many of the attractions (like the Reservoir Cruise and the Amazon River Quest) close early.
So I left the Zoo early in order to see the River Safari. I could have spent longer at the zoo, but as the day had gone on and the time was approaching to leave for the River Safari, I started to hurry past some densely vegetated exhibits - like the primates - and in some exhibits where I couldn't see the occupant I just kept walking. As it was, I missed a Penguin exhibit and I suspect a couple of other exhibits too. So I could have happily spent another half day at the zoo, then spent a relaxed half day at the River Safari, instead of racing through it before darkness fell like I did this time.
I made the mistake of doing the Zoo, River Safari and Night Safari all in the one day. 20 years ago I could have easily managed it, but this time I found it too much and I left the Night Safari at 9:00pm after only about 90 minutes, completely exhausted and with some aching muscles. Next time I'll do the Night Safari on it's own.
Hix