See these definitions
to fetch: to go to another place to get something or someone and bring it, him, or her back:
[ + two objects ] Could you fetch me my glasses/fetch my glasses for me from the other room, please?
I have to fetch my mother from the station.
This glass has been used - please fetch me a clean one.
Would you like to wait out here, and the doctor will come and fetch you in a minute?
She fetched another chair from the dining room.
He fetches the children from school on Mondays and Fridays.
That looks uncomfortable. I'll go and fetch a cushion for you.
to bring: to take or carry someone or something to a place or a person, or in the direction of the person speaking:
"Shall I bring anything to the party?" "Oh, just a bottle."
[ + two objects ] Bring me that knife/Bring that knife to me.
Can you help me bring in the shopping (= take it into the house)?
The police brought several men in for questioning (= took them to the police station because they might have been involved in a crime).
When they visit us they always bring their dog with them.
I'll see if Louisa will bring her guitar to the party.
Please remember to bring a mat and a towel with you to the next aerobics class.
Is it okay if I bring a friend to the party?
The waiter brought the menu and the wine list.
I brought him some sandwiches because I thought he might be hungry.
Say there are 2 situation.
Situation 1: Tom & Mary are in a room. A ball is right next to Mary.
Tom should say "Bring the ball to me", right?
Situation 2: But if the ball is 3 meters far from Mary's position.
Tom should say "Fetch the ball for me", right?
But many people, especially American people think "Fetch" is rude. But if they don't want to use the word "fetch", then they have to use a much longer expression "go get the ball & bring it to me".
Would American say "bring the ball to me" in Situation 2? But then the word "bring" doesn't carry the meaning "going to someplace..."
So, how do American people express themselves in this situation?