The Difference Between “Both” and “Each.”

You need a context to be able to tell whether “each” refers to two things. For example, you could say that each hand has a glove on it, or each team member was in uniform.

Let’s assume the context implies two things. You still have an important difference between these two words:

“Both” refers to two things together.
“Each” refers to two things separately.

Here’s a good example of getting it wrong:

There is one [polar vortex] at both poles, and other planets have them too. 

https://www.forbes.com/sites/marshallshepherd/2019/01/23/4-weather-concepts-that-confuse-people-did-polar-vortex-make-the-list

Sorry, each pole gets its own vortex.

Just for grins, here’s a Hubble photo of Saturn’s polar vortex.

Related image
www.themarysue.com/saturn-polar-vortex