Generally speaking, 乳ru3 is a word in ancient Chinese and a word-forming morpheme in modern Chinese , and 奶nai3 is a modern word and morpheme.
In modern Chinese, ru3 is used only as a free morpheme to form compound words, such as 乳房(mamma, breast, udder )、乳头( mammilla, nipple, teat )、乳腺(mammary gland), 乳罩(aslo 胸罩, brassiere ) , 乳汁(milk) ; 乳名( a Child's pet name); 乳制品(dairy produce), 乳品厂(dairy/milk plant), 乳脂(milkfat); 乳糖(lactose). Ru3 is chiefly used in science/technology, industry and literature.
奶nai3 is commonly and frequently used in daily Chinese. You say 奶子(vulgar, privately
used) but not 乳房;奶头,but not 乳头; 小名,but not 乳名;奶水( milk, concerning mothers' supply to babies ),but not 乳汁(no 乳水); 吃奶, not 吃乳;牛奶, not 牛乳; 奶粉, not 乳粉; 奶瓶,not 乳瓶, etc.
But nowadays except scientific terminology, nai3 is used more than before. For example, 乳罩 can also be called 奶罩,乳酪 also 奶酪, 乳制品 also 奶制品, etc.
Etymologically, 乳ru3 and 奶nai3 are cognate words.
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▲ 现代汉语词典(第五版)
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▲ 现代汉语词典(第四版)(The Contemporary Chinese Dictionary: Chinese-English edition)
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▲ 新华字典(第十一版)
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