The Wikipedia article which you drew that definition from says (right under the title):
Not to be confused with Search and rescue dog.
From that article:
The use of dogs in search and rescue (SAR) is a valuable component in wilderness tracking, natural disasters, mass casualty events, and in locating missing people. Dedicated handlers and well-trained dogs are required for the use of dogs to be effective in search efforts. Search and rescue dogs are typically worked, by a small team on foot.
Search and rescue dogs detect human scent. Although the exact processes are still researched, it may include skin rafts (scent-carrying skin cells that drop off living humans at a rate of about 40,000 cells per minute), evaporated perspiration, respiratory gases, or decomposition gases released by bacterial action on human skin or tissues.
So a search and rescue dog is the term you're looking for. On the same web page you'll find that these SAR dogs are also further classified according to specific criteria.