A 'normal' chart is usually based on a list of data in cells. To apply filters, sorts, and calculations over these types of charts requires changing the source data cell formulas or entries. Changes to the chart do not flow back to the data.
A Pivot Chart is linked to a PivotTable bidirectionally. Filters, sorts, and data rearrangements applied to Pivot Charts are also applied to their associated PivotTable and vice versa. Slicers can also be applied to PivotCharts and a single slicer can be applied to multiple PivotTables/PIvot Charts if the PivotTables/Pivot Charts are based on the same data providing us multiple view points over a single data set.