Hi, to best of my knowledge, I don't think we can partially verify connectivity of geometric network, because once created, geometric network automatically maintains connectivity as a whole. It continuously updates its network connectivity during edits based on the connectivity rules set (ArcObjects Help for .NET developers ).
"For a geometric network in a Personal or File Geodatabase, CheckandRepairConnectivity will work against the entire geometric network" (ArcObjects Help for .NET developers )
As to the difference with IGeometricNetworkErrorDetection.DefectNetworkErrors, according to the documentation, "While the DetectNetworkErrors method will discover network features with inconsistent connectivity, it does not perform an exhaustive verification. The IGeometricNetworkConnectivity2::CheckandRepairConnectivity method performs a more exhaustive check for network inconsistencies." (ArcObjects Help for .NET developers )