Differences Between Free Characteristics and Filter

Filters and Free characteristics are two similar methods to restrict the data in BW, and both restricts the values of characteristics in the query.
The difference between Free and filter, with the filter we cannot see the restricted data in the query and we cannot drilldown conversely which a free character a user will be able to navigate( Drill down and Drill across)
If you created the filter in the filter panel then that restricted characteristic values and the characteristic wont be displayed in the query result, hence no drill down drill across.
But if you create filter in Rows, Columns, Free characteristic panel, then the restricted character and the values will be displayed and hence drill down and drill across is possible.

Differences Between Filter and Restricted Keygure:
These are 2 similar methods to restrict the data in BW. A filter restricts entire query all fields, while the restricted keyfigure restricted only the selected  key figure value.
A filter restricts char values, where as a restricted keyfigure restricts keyfigure value. By default a filter is called as Restricted Characteristic.