While saving a filter, you save the filter criteria only, whereas while saving a search result, you are saving the filter criteria and the results of the search. Saving a filter helps you save time if you normally use several filters to narrow your shortlist of properties. Retrieving all the filters and applying them on a new geographical area saves time and effort, and improves productivity.
Adding filter parameters to the search
Applying filters like Bath and Bed
No need of wasting the time by adding the same filter criteria again and again for different addresses.