Maybe this drawing will make it clearer?
The length of a fat quarter yard (FQ) should always be at least 18 inches.
Not all fabrics are 45 inches wide - some are as narrow as only 40 inches - so the width of the FQ will only be half of the width of the fabric - so may vary from 20 to 22.5 inches.
A "regular" or "skinny" quarter (1/4) yard should always be at least 9 inches long - and the width of the fabric.