REGEXP_MATCH() AND REGEXP_EXTRACT() are both used for pattern matching, bu the main difference is that REGEXP_MATCH() after matching would return true or false to check if field/string matches with pattern whereas REGEXP_EXTRACT() would return the string that matches the pattern as a output.
REGEXP_MATCH([Order ID],'AE-\w*-\w*-\w*') return True/False i.e Boolean Values.
REGEXP_EXTRACT([Order ID],'AE-\w*-\w*-\w*') return sub-string from String/Field. It can be used as a field separately to view data which has matched the pattern.
Both have the same syntax.
Hope this helps you.