No, size 7 kids is not the same as size 7 womens. There is a difference in the measurements between the two.
Kids sizes are generally based on the age of the child and the height. These sizes generally range from 2T (toddler) to 16 (big kids) with 8T, 10T, 12T, and 14T for the in-between sizes. These sizes have different body measurements which are usually 1-1.5 inches smaller than the women's size with the same number.
Women sizes, on the other hand, generally start from size 4 and range up to size 14. These sizes are based on the body measurements including bust and waist. These measurements can be 1.5-2 inches larger than the kids size with the same number.
It is therefore important to carefully read the tag of the clothing and take note of both the size number as well as the associated body measurements to ensure that you get the right size of clothing for yourself.
You can find detailed guides for both Men and Women sizes at the following links: