How pairplot is constructed? Based on what rule? Why people use it?
Differences:

Pairplot

If you have m attributes in your dataset, it creates a figure with (m)x(m) subplots. 

The main-diagonal subplots are the univariate histograms (distributions) for each attribute.

For a non diagonal subplot, assume a position (i,j). This plots all the samples of the dataset on a coordinate system with axes the attributes i and j. In other words, it projects the dataset on these two attributes only. This is particularly interesting to visually inspect how the samples are spread with respect to these two attributes ONLY. The "shape" of the spread can give you valuable insight on the relation between the two attributes. For example, if the samples are spread on a linear pattern, it means that the two attributes are linearly related in your dataset. But you can also visually recognize nonlinear relations, such as quadratic, etc.

Correlation (Pearson)

It is a mathematical measure of strictly LINEAR correlation between two attributes. The closer it is to 1 or -1, the stronger the linear relation. The closer it is to 0, the weaker the relation. If there is a value close to 1 or -1, then you can safely assume that these two variables are linearly connected. If it is close to 0, you can assume the absence of linear relation BUT you cannot infer anything about nonlinearities (they might exist even if correlation is very low).

The main-diagonal elements of the correlation matrix show the autocorrelation of each attribute, thus a measure of its normalized spread around its mean value.

The non diagonal elements (i,j) show the linear correlation between the attributes i and j. Usually, correlation matrix is plotted on a heatmap (seaborn) that helps with the visualization.

Note

If you use Pearson correlation and you find that for the selected attributes (i,j) the value is close to 1 or -1, you should expect the samples forming a straight line in the (i,j) and (j,i) subplots of your Pairplot.