Minimize and reduce are two very similar words, with subtle differences between the two. The difference rests upon the degree of smallness that you are trying to convey—in the computer world, minimizing means to bring down the open browser and have it hang out at the bottom of the screen until you are ready to bring it back up.
Reduce, on the other hand, means to diminish something or to take something away from a more significant portion of something.
For example, someone who works for an employer may have an issue when their boss decides to reduce their paycheck by a certain amount. Minimize could also mean you are disregarding someone in some way.
For example, someone could say that they’re performance is minimized at their job; therefore, they are contemplating quitting. Reduction, on the other hand, doesn’t necessarily always have to be negative. It could just be that you are taking away an unwanted amount of something.