The graph on the right is popular among pop development economists. But it doesn’t tell us what most people think it does.
In addition to experiencing a different form of colonialism than Ghana or India did, receiving lots of Western aid for geopolitical reasons, and having access to markets in Japan and the US, South Korea also had a much longer history of ethnically and socially unified statehood than either Ghana or India before colonization.
Here is a summary of the mechanisms involved from Bockstette, Chanda and Putterman (2002):
A longer history of statehood might prove favorable to economic development under the circumstances of recent decades for several reasons. There may be learning by doing in the ways of public administration, in which case long-standing states, with larger pools of experienced personnel, may do what they do better than newly formed states. The operation of a state may support the development of attitudes consistent with bureaucratic discipline and hierarchical control, making for greater state (and perhaps more broadly, organizational) effectiveness. An experienced state like China seems to have been capable of fostering basic industrialization and the upgrading of its human capital stock even under institutions of government planning and state property in the 1960s and 1970s, whereas an inexperienced state like Mozambique sowed economic disaster when attempting to pursue similar policies a few years later. Such differences may carry over to a market setting — contrast, for instance, the late 20th century economic development of Japan and South Korea, modern countries with ancient national histories, with that of the Philippines, a nation that lacked a state before its 16th century colonization by Spain.