Quick quiz! What's the difference in the quick search bar on the admin members list page and the search function in the frontend member directory?
Backend members list:
Frontend member directory:
Answer: The backend members list and the frontend member directory have different purposes and parameters, and therefore, likely won't match in a 1:1 comparison.
On the backend members list, the search bar functions as a "quick search" to be able to quickly find a single member so an admin can easily get to that member's record - it solely looks at the name, email, or the first line of a member's address. It's not meant to query groups of members since admins can create groups and/or reports to pull those things.
On the frontend member directory, website visitors searching are likely trying to find groups of members (by keyword for example), rather than just one particular member a majority of the time, so there are different search criteria available - name, parent name, professional title, custom field values from the member records, and text a member adds to their description.
It's also important to note that the frontend directory is based on a group with limitations, usually current members only, while the backend member list is going to search any record in the system (unless you're also using the filters).
If your goal as an admin is to query certain groups of members, we can help you get groups or reports created to do that, just ask!