Not all of the states during the Warring States period were ruled by nominal kings. So they cannot be translated, strictly speaking, as “kingdoms.” This may seem like a matter of semantics to us, but whether a sovereign at the time was a viscount, a duke, or a king was of great political, and therefore historical significance.

The Warring States of the eponymous period (475 – 221 BC) were indeed hereditary patriarchal monarchies. But they all began as feudal grants by the Kings of the Zhou Dynasty in order to better govern China (in a system comparable to feudalism in medieval Europe).

The State of Chu, for example, was originally granted by King Cheng of Zhou in the 11th century BC to the Xiong clan, whose ancestor had once been the tutor to the grandfather of the King. The title bestowed to the Xiong clan, however, was not “King” (王) but Viscount (子). So the State of Chu was really at first the Viscountcy of Chu (though no one ever seems to bother with that distinction as the entity is always referred to as the “State of Chu”).

400 years later (700 BC), the ambitious 17th Viscount of Chu, Xiong Tong was not satisfied with the lowly title of viscount. He convened a meeting of regional nobles to discuss the advancement of his hereditary title. When the Marquis from the neighboring State of Sui did not show, Xiong Tong declared war and defeated the Marquis of Sui. Xiong Tong hence declared himself to be the King of Chu, marking Chu’s de jure independence from the Kings of Zhou. The Zhou Dynasty’s power was greatly reduced at the time, and so did not militarily contest the declaration.

This episode is significant because it was the first instance in which one of the seven Warring States (Chu, Qi, Wei, Yan, Han, Zhao, and Qin) would renounce its fealty to the Zhou Dynasty. It wasn’t until more than 350 years later, well into the Warring States period, that the other six states (all ruled then by dukes) would declare themselves nominally to be King.

So, the Warring States really consisted of six warring dukedoms and one kingdom, until about around 300 BC, when the six dukedoms upgraded themselves to kingdoms.

It’s worth pointing out that the distinction between "kingdom" and "state" primarily exists in translation. In Chinese, the Warring States period and Three Kingdoms period are “Zhan Guo” (战国) and "San Guo" (三国), respectively. The second Chinese character in each term, "Guo" (state) is identical. However, it would be incorrect to call “Zhan Guo” “Warring Kingdoms” because the participants were not all kingdoms, where as the principal players in the Three Kingdoms period were all kings.

Source: The history of the House Xiong of Chu can be found in the 10th Genealogy of the Annals of the Grand History by Sima Qian.

From a quick perusal of Wikipedia its more a definition of state and kingdom that marks the difference. A state unlike a kingdom does not require someone of nobility to be at its head.

Example would be France that is a state while England can be considered a kingdom (but the term is extremely outdated now).

The reason why there were states was due to the division of China into states which reported to a central leadership. However the central power lost its actual power and the states battled with each other for control of land and economic resources.