Mobile Pages Should Be Equivalent to Desktop Pages
Mobile versions of pages should be equivalent to the desktop pages, with the same functionality and main visible content, but the layout can be different.
Mobile Pages should be Equivalent to Desktop
Desktop and mobile pages have to fulfil the same purpose and contain equivalent content, but there isn’t currently any ranking impact as Google is only really checking to see if the mobile page can be returned.
Redirect Deprecated Mobile Sites
If you want to remove a mobile site because you now have a responsive site, you should ideally redirect to manage bookmarks for users, but Google doesn’t really care as they’ll drop the mobile URLs when they recrawl the desktop URLs without the mobile rel tag.
Mobile Sites Don’t Need Sitemaps
Separate mobile sites should be canonicalising to the desktop page, so you don’t need to submit them to Google via a Sitemap, but it’s still worth adding to Search Console.
Mobile Sitemaps Are Not for Smartphone Pages
Mobile sitemaps are for feature phone pages only, not smartphone compatible pages. If you have smartphone URLs which are different to the desktop URLs, use a normal XML sitemap with rel=alternate.