Begin by asking a single question: what is being counted on each axis? Both the average alcohol consumption and the cirrhosis death rate are computed for an entire nation, and there are 10 nations giving 10 dots on the scatter plot. Whenever the observation is a population summary rather than a person, the design is correlational at the group level.
The four classic analytic designs differ by their unit of analysis. Cohort, case-control and cross-sectional studies all collect exposure and disease status on named individuals. Only the ecological design uses aggregated, population-level figures and correlates them across groups.
Mechanism of inference: by lining up 10 countries, the investigator looks for a trend (more drinking $\rightarrow$ more cirrhosis). This generates a hypothesis cheaply from routine data, but the conclusion cannot be transferred to individuals — doing so risks the ecological fallacy. Confounding by country-level factors (diet, healthcare access, reporting) is also uncontrolled.
Therefore the matched description is the group-correlation design. To be sure, contrast it with the alternatives one by one: a cohort would enrol drinkers and non-drinkers as people and watch who develops cirrhosis; a case-control would take cirrhosis patients and disease-free people and ask each how much they drank; a cross-sectional survey would measure drinking and liver status in the same individuals at one moment. Every one of these counts persons. Only the present design counts countries, so it stands apart as ecological.
\[\boxed{\text{Ecological (correlational) study}}\]