A cross-sectional study measures disease and risk factor prevalence in a sample of individuals in a population in a defined time period, mainly to explore the burden of disease but also to generate associations.
A cohort study consists of a sample of individuals in a population followed up over time to observe changes in health status, to measure disease incidence, and to examine associations between risk factors and health outcomes.
A trial is similar in design to a cohort study except that the investigators impose an intervention on one or more of the study populations.
The ecological 'design' is really a mode of analysis based on variables being applied to places rather than individuals, rather than a design.
There are conceptual and practical interrelationships between various study designs.