Both means “the one as well as the other,” when the two are considered together.
Each refers to the individual members of a group considered separately.
My bank requires the signatures of both people to cash a check made out to Mr. and Mrs. Perdue.
My bank requires a separate deposit form for each of our accounts.
When do you use “both” and when do you use “the two”?
I ran across an example today where the latter should have been used.
The difference between both economic forecasts was used to calculate NPV of the pilot project.
The word “both” serves to merge the two forecasts in question or stress their similarity, but that is not the case in this example. Use “the two” when you wish to differentiate them or make a reconciliation or rapprochement.
The difference between the two economic forecasts was used to calculate NPV of the pilot project.
Personal Note: Whenever I’m asked whether I want apple pie or pumpkin pie, I always answer “Both.”