What is the difference between 抓 and 捉?
抓 and 捉 can be used interchangeably when it means 'catch; capture; arrest'

For example:
抓老鼠 = 捉老鼠 = catch/capture mice
警察來抓人 = 警察來捉人 police come to arrest someone
In the context of 'catch; capture; arrest' , 抓 is more colloquial, 捉 is more literary

抓 contains the meanings of 'get hold of/grab; seize'
which it doesn't share with 捉

Example:
抓緊這個機會 (get hold of this opportunity) cannot be written as 捉緊這個機會 because  'get hold of' is different from 'capture/catch'
抓起武器 (grab weapon) cannot be written as 捉起武器 because 'grab' here refers to 'get hold of', not 'capture/catch'
抓權 (seize power) cannot be written as 捉權 because 'seize' here refers to ''get hold of', not 'capture/catch'

抓 also contains the meanings of 'to scratch'
which it doesn't share with 捉

Example:
抓癢 (scratch an itch)
抓眼珠 (scratch eyeball)
Also: 抓狅 (catch a madness = become crazy) cannot be written as 捉狅  because '抓狅' is a set phrase; 捉姦 (catch an affair in action) cannot be written as 抓姦 because '捉姦' is a set phrase