Malay is a race. A malay person can stop being muslim and still be a malay.
muud is a race in Singapore. If a sinkie muud renounces islam, he is still a muud in Singapore.
In jiuhu, muud is an identity, not a race. To be muud in jiuhu, one must be a moslem. It's in the jiuhu constitution. The bumiputras of Sarawak are not muud. They are bumi.