Duplicate Rule vs Duplicate Job

Duplicate Rule -

Duplicate Rule is what is responsible for the 'We found 10(example) number of potential duplicates for this record' when we view a record that is a duplicate rule defines what happens when a user views a record with duplicates or starts creating a duplicate record. 

Salesforce provides standard duplicate rules for business and person accounts, contacts, and leads. We can also create duplicate rules.

Reference - https://help.salesforce.com/s/articleView?id=sf.duplicate_rules_map_of_reference.htm&type=5

Duplicate Job -

Duplicate Job searches across the entire org. for duplicates based on the matching rule created. This is generally a batch job and this will list all duplicates as per the matching rule.

Reference - https://help.salesforce.com/s/articleView?id=sf.duplicate_jobs_run_and_manage.htm&type=5