The WordPress comment system is way more complex than you might expect. For this reason, it ends up confusing a lot of WP users.
The Discussion settings can only be used to disable comments (and pingbacks and trackbacks) for future posts you publish. For existing posts (and pages), you can disable comments via the post editor.
If you visit the Posts menu in your dashboard, you can use the bulk actions dropdown to turn off comments on many posts all at once. The other benefit of this method is that you can still display comments that you’ve already approved while removing the comment form.
And, the Disable Comments plugin is an excellent alternative if you want to quickly remove all comments and the comment form from all of your posts and pages.