Four designs and the direction they look
A cohort study starts with exposure status and follows groups forward in time to see who develops the outcome, which suits estimating incidence and relative risk. A case-control study starts from the outcome and looks backward, comparing the past exposures of cases and controls, which is efficient for rare diseases. A cross-sectional study takes a single snapshot, measuring exposure and outcome together, good for prevalence but weak on timing.
An ecological study compares groups rather than individuals, relating average exposure to average outcome across populations, which is cheap but prone to the ecological fallacy of inferring individual risk from group data.
What each design can and cannot establish
None of these designs randomizes exposure, so all are vulnerable to confounding and can show association without proving causation. Their relative strengths trade efficiency against the ability to establish temporal sequence and rare-event detection.
This is general educational information, not medical advice. Study design quality is one factor in weighing evidence, and clinical conclusions should be drawn with qualified professional input.