They're right next to each other, but the zoo is open during the day, and the night safari at - well, you know Definitely some overlap in terms of the types of animals, but if this is your sort of thing, I'd do both. You could make a long day of it and do both, if you don't mind putting that many miles on your feet. There is also Jurong Bird Park, but that's in a totally different part of town. Perhaps an activity for a different day if you are into the animals.

Taxis are relatively cheap. The train system (MRT) also usually works pretty well - they've had some rather unusual outages in recent weeks. If you take the train, the Orchard station is in the ION shopping mall, at the corner of Orchard and Scotts - take it to Ang Mo Kio, then get a bus to the zoo (can't remember the number, but you'd be taking it from the beginning of the line to the end). If you are in town for more than a short time, you might want to buy an EZ-link card, which lets you ride the train and the bus. It includes a non-refundable deposit, but also gets you a discounted ride relative to paying for each one individually. Available at any station. If you stay at the night safari until the bitter end, you might have a problem with the last bus to Ang Mo Kio not making it until after the trains have stopped - I'd have to check the schedule to make sure. Or just take a taxi. There's a pretty good chance you'd have to stand on the bus for at least part of the trip, so if that is not appealing, taxi is the alternative. The train system does not go near the zoo.

Orchard Road, at least as of a few days ago, had Christmas lights and trees everywhere, kids might be into that sort of thing. Lots of adults seem to want their pictures taken there too.