An overview of all relevant tables:

Please note: course_modules.instance = grade_items.iteminstance.

The id in the URL of a course module is the course_module.id. This can be used to acquire a grade for a specific user. The following query is an example. All you need is the course_module id and the student's user id.

SELECT * FROM mdl_grade_grades
WHERE userid = //copy the student id here//
AND itemid IN (
    SELECT id FROM mdl_grade_items
    WHERE iteminstance IN (
        SELECT instance FROM mdl_course_modules
        WHERE id = //copy the course module's id here//
    )
)

In other words: the mdl_grade_items.iteminstance column does not refer to the mdl_course_modules.id column, but to the instance id instead.