The word that we use for the room where food is prepared in both British and American English is "kitchen." There is no difference whether this room is at a restaurant or in someone's home. I hope that this helps. :)
英語でもキッチンのままで通じます。綴りはKitchenです。
他の単語で表現されているのは聞いたことがないです。
I love my kitchen.(私はうちのキッチンがお気に入りです）
My mom is cooking lunch in the kitchen.(お母さんはキッチンで昼食を作っています）
少しでも参考になれば幸いです。
"Kitchen" is the term given to the room in a house were you will make food preparation, cook and often store ingredients and food.
ex. "I need to clean my kitchen because it is so dirty"
"I have spent all day in the kitchen preparing tonight's main course meal!"
prep = preparation.
"Kitchen" は 家の中で食事の支度や調理をする場所をいいます。食べ物もここに保管されていることが多いです。
例：
"I need to clean my kitchen because it is so dirty"
（キッチンが汚れているから掃除しないと）
"I have spent all day in the kitchen preparing tonight's main course meal!"（今夜のメインを作るために朝からずっとキッチンにいました）
prep = preparation.（準備）
Kitchen is the basic word for the place where you prepare and cook food.
Cooking area can also be used but it is not used as frequently as kitchen.
A kitchenette is a small ktichen, some small apartments or homes will not be able to fit an entire kitchen so they would instead have a kitchenette.
The place where we prepare food in the house is called a kitchen.
Example sentences:
She is in the kitchen cooking egg fried rice.
The restaurant's kitchen was very busy today.
家の中で食事の支度をする場所のことは "Kitchen" といいます。
例文：
She is in the kitchen cooking egg fried rice.
（彼女はキッチンで卵チャーハンを作っている）
The restaurant's kitchen was very busy today.
（そのレストランは今日はキッチンがすごく忙しかった）
キッチンはそのままkitchenですよ。
日本の家のキッチンが狭すぎて料理ちゃんとできないですよ。
このキッチンは私のところだから入らないで
This kitchen is my space so dont come in!
キッチンは汚いからあまり使ってない
The kitchen is so dirty so I dont really use it
This is the kitchen in English and this is the word we use for the room in which food is prepared or cooked.
However there are some other words we can use to describe rooms that involve food and cooking
For example we have a larder, and this can be used to describe rooms in restaurants that prepare sweet food, or a room used to store food. This can be applied to a home too.
We also have the word pantry which is similar to larder.
イギリス 
アメリカ合衆国 
日本 
南アフリカ 
