The longitudinal study uses time as the main variable, and tries to make an in depth study of how a small sample changes and fluctuates over time.
A cross sectional study, on the other hand, takes a snapshot of a population at a certain time, allowing conclusions about phenomena across a wide population to be drawn.
An example of a cross-sectional study would be a medical study looking at the prevalence of breast cancer in a population. The researcher can look at a wide range of ages, ethnicities and social backgrounds. If a significant number of women from a certain social background are found to have the disease, then the researcher can investigate further.
This is a relatively easy way to perform a preliminary experiment, allowing the researcher to focus on certain population groups and understand the wider picture.
Of course, researchers often use both methods, using a cross section to take the snapshot and isolate potential areas of interest, and then conducting a longitudinal study to find the reason behind the trend.
This is called panel data, or time series cross-sectional data, but is generally a complicated and expensive type of research, notoriously difficult to analyze.
Such programs are rare, but can give excellent data, allowing a long-term picture of phenomena to be ascertained.