Little Kingdom of Hyrule
The manual for the original Legend of Zelda places the game in "a little kingdom" in the land of Hyrule. The Japanese specifically states that the little kingdom is part of the "Hyrule region". This indicates that Legend of Zelda's Hyrule is just a small part of a greater georgaphical territory collectively known as Hyrule.
The Little Kingdom as part of Adventure of Link's Hyrule
Though commonly refered to as "North Hyrule", it's believed by many theorists that the Hyrule seen in Adventure of Link is the Hyrule region spoken of in the Legend of Zelda manual. Thus, the little kingdom is part of Adventure of Link's Hyrule, and not just a territory south of it.
Theorists point to the southwestern corner of the Adventure of Link map as being the little kingdom, because of the existence of several common landmarks. Both territories contain a Death Mountain, Spectacle Rock, graveyard, twin ponds, sideways L-shaped forested area, mazelike forested area, and a eastern side that borders water.