A 308 Permanent Redirect is a server HTTP response status code used for permanent redirection.
A 308 HTTP response is near identical to a 301, and has been confirmed to be treated as such by Google.
The only notable difference between a 301 and 308 HTTP response is that a 308 does not allow changing the request method from POST to GET.
HTTP/1.1 308 Permanent Redirect
Content-Type: text/html; charset=UTF-8
The document has been moved to <a href="https://www.example.com/">https://www.example.com</a>
RFC7538, April 2015
A 308 HTTP response has been confirmed by Google to be treated as identical to a 301 by its bots/algorithms.
However a 308 response is still a newer and more unusual status code, so it is unknown how all search engines/bots around the world will treat it.
It should be noted that some sites may use a 308 status code in a non-standard way, such as in Google Drive - where a 308 Resume Incomplete status is used to indicate when an incomplete upload has stalled.