Speaking only of American shoe sizes, women's are two numbers higher than men's. I wear a 9 men's and 11 women's. Normal width for men is D; narrow men's is B. Normal width for women's is B, wide is D, and narrow is usually AA.
As Kyril said, the shoes should fit properly or you are going to have trouble with your feet (and legs and hips and back). Try the shoes on and walk up and down in them on carpet. They should be comfortable. They can be snug but should not bind or force the bones of your feet to be out of natural alignment.
When I changed my wardrobe I went nuts and bought bunches of shoes. They are all 11B, but some I can't wear for more than four hours at a time. Others I can wear day after day. I can wear some really cute ones for a day but have to wear others the next day to let my feet recover. (Ah, the travails of womanhood...

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- Kate