Previous/Next post should show posts from same category

The next/previous links are core WordPress functionality and don’t provide the default functionality of linking within a category only.

The core calls are in the single.php template, which can be customized using a child theme.
Edit the core previous_post_link() and next_post_link() calls.

Hiding the links is even simpler with a bit of CSS:

.single #nav-below {
    display: none;
}