Pooled analysis combines time series for several cross-sections. Pooled data are characterized by having repeated observations (most frequently years) on fixed units (most frequently states and nations).
Both pooled cross sectional data and pure panel data collect data over tine (this can range from 2 time periods to any large number). They key difference between the two is the "units" we follow. I am defining units as households, countries, or whatever we are collecting data on.
In pooled cross section, we will take random samples in different time periods, of different units, i.e. each sample we take, will be populated by different individuals. This is often used to see the impact of policy or programmes.
For example we will take household income data on households X, Y and Z, in 1990. And then we will take the same income data on households G, F and A in 1995. Although we are interested in the same data, we are taking different samples (using different households) in different time periods.
In pure panel data, we are following the same units i.e. the same households or individuals over time. For example we will follow the same set of households X, Y and Z, for each time period we collect data i.e. in 1990 and we will also interview the same households in 1995.