If you put Anchor in Display Settings to yes this category shows all of the products of its own and all of its subcategories in the frontend.
Therefore the 13 products you see are a subset of what you see in frontend (if all of this 13 products have the right visibility and are saleable of course).
The 17 in the category tree is the sum of all unique products of the category itself and the products of subcategories (given the fact that Anchor is enabled). So if you have some products in the category itself and in one of the subcategories this product is counted only once.
You can check if everything is ok in your system with that category by running this SQL statement:
select count(distinct product_id) from catalog_category_product where
category_id in (
select entity_id from catalog_category_entity where parent_id = [YOUR
If the result is 17 everything is fine.
I hope that helps.