What is the syntax of "search" and "where" in PHP API?

I’ve missing deeper explanation and more examples when it comes up to filter out something using the PHP API. What is the right syntax? What is possible to do here?
https://developer.mautic.org/#list-contacts

Could it be, “search” is simply the same as one puts into the searchbox of the WebGUI?

Search Help
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Search Operators:
+ (plus sign) - Search for the exact string (i.e. if admin, then administrator will not match)
! (exclamation mark) - Not equals string
" " (double quotes) - Search by phrase
( ) (parentheses) - Group expressions together.
OR - By default the expressions will be joined as AND statements. Use the OR operator to change that.
% - Use the % as a wildcard to search for specific names or values in a phrase (i.e. to find all companies with the word ‘Technologies’ then type %technologies%)

Search commands
is:anonymous
is:unowned
is:mine
email:*
segment:{segment_alias}
name:*
company:*
owner:*
ip:*
ids:ID1,ID2 (comma separated IDs, no spaces)
common:{segment_alias} + {segment_alias} + ...
tag:*
stage:*
email_sent:EMAIL_ID
email_read:EMAIL_ID
email_queued:EMAIL_ID
email_pending:EMAIL_ID