对(duì), 双(shuāng) and 副(fù) can all be translated as "a pair" in English, but they modify different objects in Chinese

对(duì) 

It refers to two people who are doing something together or have a particular relationship, or two animals or birds of the same species that mate with each other, or two objects that match each other in style or function.

 

一对翅膀 (yí duì chìbǎng): a pair of wings  

一对鸳鸯 (yí duì yuānyang): a pair of Mandarin ducks

一对夫妻 (yí duì fūqī): a couple

双(shuāng)

双(shuāng) also means "even", and it is the antonym of 单(dān odd). It is used to refer to objects that naturally come in pairs.

 

一双眼睛 (yì shuāng yǎnjing): a pair of eyes

一双手 (yì shuāng shǒu): a pair of hands

一双皮鞋 (yì shuāng píxié): a pair of leather shoes

副(fù) 

副(fù) refers to certain objects whose function depends on two constituting parts. Sometimes it used for the complete set of things, maybe two or more. Some objects can be modified by more than one measure word such  as 一副耳环(yí fù ěrhuán  a pair of earrings) or 一对耳环(yí duì ěrhuán  a pair of earrings)

 

一副扑克 (yí fù pūkè): a deck of playing cards

一副眼镜 (yí fù yǎnjìng): a pair of glasses

一副手套 (yí fù shǒutào): a pair of gloves

 

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