301, 302, 307 and 308
301 and 308 say the move is permanent: Google moves the old URL's signals to the new one and indexes the new URL. 302, 303 and 307 say it is temporary: Google keeps the old URL in mind and may keep showing it. 307 and 308 keep the request method (a POST stays a POST); for crawlers that is the only difference. A temporary redirect left in place for months is usually treated as permanent in the end, but don't count on the timing.
Why redirect chains matter
Chains build up over time: http to https, then to www, then to a trailing slash, then to the new URL from the last migration. Googlebot follows up to 10 hops and then gives up; every hop is one more request and slower recrawls. Redirect each old URL straight to its final address and link to the final URL in menus, sitemaps and canonicals.
After the redirect
The last URL is the one that gets indexed, so it must return 200 and be indexable. Check it with the noindex checker, and its canonical with the canonical checker. If Search Console lists the old URLs as Page with redirect, the guide to that status explains when that is fine.
We fetch the URL with GET, as NoindexWatchBot, and follow up to 5 redirects. JavaScript redirects are not run. Some sites redirect bots or other countries differently. Results are not stored.