Both … and
Two things together
Mom is going to the cinema. Dad is going to the cinema.
Both Mom and Dad are going to the cinema.
They bought potatoes. They bought meat.
They bought both potatoes and meat.
There are two shirts. You can have both this one and that one..
Either … or
One of two things
Mom and Dad have one ticket for the concert. Maybe dad will go. Maybe mom will go.
Either Mom or Dad will go to the concert.
Bread is $2.00 and butter is also $2.00 but I only have $3.00.
I can buy either bread or butter.
There are two shirts. You can have either one or the other.
Neither … nor
None of two things
Mom is not going to the cinema. Dad is not going to the cinema.
Neither Mom nor Dad are going to the cinema.
I did not buy bread. I did not buy butter.
I bought neither bread nor butter.
There are two small shirts. Neither one nor the other will fit you.