The time series data contain a sequence of data collected at discrete and equally spaced intervals of time (daily, weekly, monthly, quarterly, annually, etc.). For example, historical returns of an equity index. The time period and the length of the equally spaced time interval can be short or long. Both short and long time periods can be ideal as per the analysis.
The cross-sectional data contain the observations representing different characteristics at a single point in time. For example, P/E ratios of 500 companies in an index at a particular time. It is useful in sector-specific analysis.
We must use a random sample whether we deal with time-series data or cross-sectional data.
Some types of data can have both time-series and cross-sectional aspects. Panel data and longitudinal data have both time-series and cross-sectional aspect.
The panel data consist of observations through time on a single characteristic of multiple observational units. For example, annual EPS of 50 companies for a period of five years.
The longitudinal data consist of observations on characteristic(s) of the same observational unit over different time periods. For example, annual earnings growth and annual revenue growth for a company over a period of five years.
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