What’s the difference between HTTP 301 and 308 status codes?

An overview of 301, 302 and 307

The RFC 7231, the current reference for semantics and content of the HTTP/1.1 protocol, defines the 301 (Moved Permanently) and 302 (Found) status code, that allows the request method to be changed from POST to GET. This specification also defines the 307 (Temporary Redirect) status code that doesn’t allow the request method to be changed from POST to GET.

See more details below:

6.4.2. 301 Moved Permanently

The 301 (Moved Permanently) status code indicates that the target
resource has been assigned a new permanent URI and any future
references to this resource ought to use one of the enclosed URIs. […]

Note: For historical reasons, a user agent MAY change the request
method from POST to GET for the subsequent request. If this
behavior is undesired, the 307 (Temporary Redirect) status code
can be used instead.

6.4.3. 302 Found

The 302 (Found) status code indicates that the target resource
resides temporarily under a different URI. Since the redirection
might be altered on occasion, the client ought to continue to use the
effective request URI for future requests. […]

Note: For historical reasons, a user agent MAY change the request
method from POST to GET for the subsequent request. If this
behavior is undesired, the 307 (Temporary Redirect) status code
can be used instead.

6.4.7. 307 Temporary Redirect

The 307 (Temporary Redirect) status code indicates that the target
resource resides temporarily under a different URI and the user agent
MUST NOT change the request method if it performs an automatic
redirection to that URI. Since the redirection can change over time,
the client ought to continue using the original effective request URI
for future requests. […]

Note: This status code is similar to 302 (Found), except that it
does not allow changing the request method from POST to GET. This
specification defines no equivalent counterpart for 301 (Moved
Permanently) (RFC 7238, however, defines the status code 308
(Permanent Redirect) for this purpose).

The need for 308

The RFC 7238 has been created to define the 308 (Permanent Redirect) status code, that is similar to 301 (Moved Permanently) but does not allows the request method to be changed from POST to GET.

The 308 status code is now defined by the RFC 7538 (that obsoleted the RFC 7238).

3. 308 Permanent Redirect

The 308 (Permanent Redirect) status code indicates that the target
resource has been assigned a new permanent URI and any future
references to this resource ought to use one of the enclosed URIs.
Clients with link editing capabilities ought to automatically re-link
references to the effective request URI to
one or more of the new references sent by the server, where possible. […]

Note: This status code is similar to 301 (Moved Permanently),
except that it does not allow changing the request method from
POST to GET.

Se we have the following:

                                                             +-----------+-----------+
                                                             | Permanent | Temporary |
+------------------------------------------------------------+-----------+-----------+
| Allows changing the request method from POST to GET        | 301       | 302       |
+------------------------------------------------------------+-----------+-----------+
| Doesn't allow changing the request method from POST to GET | 308       | 307       |
+------------------------------------------------------------+-----------+-----------+

Choosing the most suitable status code

Michael Kropat put together a set of decision charts that helps to determine the best status code for each situation. See the following for 2xx and 3xx status codes: