In Mail.dll email client, partial success status means, that email was successfully sent to some, but not to all recipients.
This happens when client submits email message to the SMTP server, during initial email submission. You won't see this, if server initially accepts the email, all recipients, and only later realizes it can not deliver the message to some.
You can use ISendMessageResult.RejectedRecipients
to get rejected recipients.
You also won't see this status returned, unless you set Smtp.Configuration.AllowPartialSending
to true (default is false).
Different servers act differently and verify recipients differently during email submission.
In most cases you may still need to examine bounced messages.
There are some techniques like VERP to help with that:
https://www.limilabs.com/blog/verp-variable-envelope-return-path-net
Here you can find more on parsing and handling bounce email:
https://www.limilabs.com/blog/bounce-handling