我觉得这两种说法，没有多大区别，都是黑猩猩妈妈的意思。只是强调的侧重点有所不同：

1. a mother chimp，强调 chimp，可以理解为当妈妈的黑猩猩，不是母黑猩猩的意思 （母黑猩猩是female chimp)。 

2. a chimp mother, 强调mother的特性，可以理解为黑猩猩妈妈。

在英语中，当mother指动物时，字典的解释是 A female parent of an animal，being a mother. (例：a mother bird.) 没有产子的雌性动物，应该用female + 动物名称。

请看国外英语媒体的例句：

(1) At a zoo, a sick mother chimpanzee died, leaving her baby behind as an orphan.

(2) Chimpanzee mothers at Bossou, Guinea carry the mummified remains of their dead infants.

(3) Female chimpanzees hunt with spears while lazy males wait to steal glory - sound familiar?

其他一些动物也有相似用法:

(4) Elephant mothers have a very important role as the matriarchs of their social networks, such as leading the herd to safe areas that have plentiful food and water.

(5) Typically, mother elephants and their daughters remain together in a matriarch-led herd from birth until they are separated by death.

(6) As far as scientists can tell, a female elephant needs to come into heat a second time three weeks later,