"make a change" or "make a difference"

As far as I know, "make a change" means that you are making something different than how it was. You are CAUSING something.

"make a difference" literally means that the EFFECT is different than the original.

Eg:

He made a change with his new tactics. means that he tried differently. He made a cause. It does NOT really mean that his tactics caused an effect. The result might be the same irrespective of his new tactics. His action is given emphasis.

He made a difference by changing his tactics. means that by changing his tactics, something different happened out and it would not have happened if he did not do that. The result is given emphasis.

Most times, one needs to make a change in order to make a difference, but sometimes, sadly, making a change makes no difference at all.

Here, there is a difference between the two choices and the correct answer is "to make a change".

to make a change = to make an alteration.

to make a difference = to have an effect (or no effect) on a person or situation.

"You won't lose any weight without making changes in your diet. Substituting pasta for French fries won't make any difference and you won't lose any weight."