Filter Controls are elements that can be added to any Data Studio report, using the Filter Control button in the toolbar. The default Filter Control is a multi-select pop-up type, but it can be configured in the Style pane with a number of options. Filter Controls can be single-select or multi-select, can include a Search box, can be a pop-up or clickable type, and can include filter operators such as EQUALS or CONTAINS. Of course, color, font, and size are all customizeable as well.
Data Studio Help: Filter Controls
Chart Interaction Filters allow report authors to turn charts into interactive filters. For example, if your report contained a pie chart, this could be made into an interactive filter allowing the user to click a section of the pie chart to filter the information in the report.
Data Studio Help: Chart Interaction Filters
Treemap as filter menu from Mehdi Oudjida
Data Studio Help: About Filters
Filter by Email is a relatively new feature of Data Studio that uses the user's Google account to display a custom data set based on an Email field in the data source.
Data Studio Help: Filter by email address
I created this sample report (also linked to the image above) to show examples of all the elements discussed here (except Filter by Email), so you can see how these different filters work. Obviously, you wouldn't use them all in one report for the same dimension, so this report is really just for fun.
Let me know.. how do YOU like to filter?