矮(ǎi) is used to describe one's height is short, the opposite meaning of which is 'tall'. While 短(duǎn) is used to describe the length of the item is short, the it's opposite meaning is 'long'.
For example,
他很矮，只有130公分。
Tā hěn ǎi， zhǐyǒu 130 gōngfēn
He very short, only has 130 cm
He is very short, with only 130 cm.
我的尺子很短。
Wǒde chǐzi hěn duǎn
My ruler very short
My ruler is very short
