The list in catalogue button to the right of a supplier name is only visible when there are items in the catalogue linked to the supplier. Clicking that button will list just those items.
The “list these in catalogue” button will list all items for the found set of suppliers. This can be useful when consolidating and cleaning up supplier information.
If you have an email address stored for a supplier, the “create email” button is visible and will attempt to create a new email in your email programme.