The Search Records feature will return results excluding disapproved and cancelled documents, while the individual searches in Common Tasks (Awards, Negotiations, Proposals, Subawards) will return all results, including disapproved and cancelled documents.
Additionally, the Search Records feature is limited by your access/role, whereas the individual searches are not. Search Records will only return results for items you have access to, either because you created the document, you were provided an access role to the document, you are listed as personnel on the document, or you have been provisioned as a unit viewer/approver. You should be able to open any document that appears in your Search Records results. Individual searches in Common Tasks (Awards, Negotiations, Proposals, Subawards) will return all results, regardless of access, however you will only be able to open items for which you have access.