Reduce vs Minimize - What's the difference? is that reduce is to bring down the size, quantity, quality, value or intensity of something; to diminish, to lower, to impair while minimize is to make (something) as small or as insignificant as possible.

A reader feels there’s a difference between the words minimize and reduce: Writers often use “minimize” to mean “reduce.” To minimize something is to reduce it to the smallest amount or degree. To “reduce” something is simply to make it smaller. He offers two examples of perceived misuse of the word minimize and draws a distinction: