Google chose different canonical than user [Google Search Console / Webmaster Tools]

This URL is marked as canonical for a set of pages, but Google thinks another URL makes a better canonical. Because we consider this page a duplicate, we did not index it; only the canonical page is indexed. We recommend that you explicitly mark this page as a duplicate of the canonical URL. To learn which page is the canonical, click the table row to run an info: query for this URL, which should list its canonical page.

What to do: It’s best to follow Google’s advise on this one. Please the Google gods and set their version as the canonical url.

Submitted URL not selected as canonical [Google Search Console / Webmaster Tools]

The URL is one of a set of duplicate URLs without an explicitly marked canonical page. You explicitly asked this URL to be indexed, but because it is a duplicate, and Google thinks that another URL is a better candidate for canonical, Google did not index this URL. Instead, we indexed the canonical that we selected. The difference between this status and “Google chose different canonical than user” is that, in this case, you explicitly requested indexing.

What To Do: If you are properly using canonical tags, there is nothing to do so long as you are using canonical tags to tell Google what page to prefer. It may not be necessary to include non-canonical URLs in your sitemap, but I have found it helpful as Google will index some of these non-canonical URLs and display them in the search results.