The search filters include both Partner (company) attributes and Location attributes.

When you select the “Search only HQ” radio button, location attributes are matched only against the main (HQ) location for each partner company, and at most one entry per partner is returned.

When you choose the “Select all Locations” radio button, all locations are returned for which the location attributes match AND the partner attributes for the location's partner company match.

example: if you match on country Canada, you'll get either all partners headquartered in Canada, or all locations in Canada (regardless of HQ country), depending on the radio button setting.