There is endless confusion between these two, and Sri Lankans swap the names freely. They are two different fruits. They taste close enough that it rarely matters, but they do not look alike once you know what you are looking at.
Sugar apple
Bumpy skin, sometimes green and sometimes red, knobbled like an artichoke. When it is ripe you can break it in half with your hands. Inside is creamy white flesh, soft and slightly grainy, fragrant, and full of large smooth black seeds that you separate in your mouth and spit out. Sweet enough to be addictive, and worth the faff with the seeds.
Custard apple
Thicker skin, green or yellow or red, patterned more like reptile scales than knobbles, and not hard. Same black seeds inside, easily discarded. The flesh can be juicy and creamy or on the firm side depending on ripeness.
As for the taste, the closest we can get is strawberries with a very sweet pear and a little cinnamon. It genuinely does taste of custard, which is how it got the name.
Where to buy them
Supermarkets, fruit shops and roadside stalls, all over the island. Neither is expensive. Both are worth stopping for.
More from the island is in everywhere we have been in Sri Lanka.
Two more to look for: the king coconut and the banana varieties.