You can find all the product tags associated with each catalog under 'Data' - 'Tags'. These product tags act as filters on your Elastic site. Within the tags section, you can choose the order they will be shown and turn the filters on or off by checking or unchecking the 'Filter' box. This can be done at the Tag Name (Parent) or Tag Value (child) level. You can also check or uncheck all tags on the current page by clicking the box next to the 'Filter' header.
If no position is set or the position number in admin is the same they will sort alphabetically. Using the above example you will see the filters for this catalog shown, with the lowest sort position first (top to bottom).
Parent Level:
Child Level: