The published Grades tab in the gradebook shows a summary of the scores you have published. Since your students and their parents can only see the grades you choose to publish, the scores and grades in the view match the progress reports as seen by students and parents.
In contrast, the All Grades tab shows all grades in the gradebook, published or not.
This article provides information on what do students and parents see when the progress reports are published.
Parents and students will only see the grades you publish. When publishing from multiple Gradebooks over the course of a term, students and parents will see a "Current Grades" progress report, which consists of the grades you publish from the current Gradebook. If you had published grades from other Gradebooks, those progress reports are available to students, parents and teachers via the All Progress Reports menu when viewing the current progress report.