We'd call that an 'entry way' or a perhaps mud room if it was a side entrance. A porch is an addition to the structure, supported with its own roof. They can be glassed in or open.
A fanny here refers to somebody's ass (grandma might say you need a good smack on the fanny). Across the pond I believe fannie is a crude reference to female genitalia.
EDIT: A good link if you really want to explore the differences - http://www.effingpot.com/