ctime refers to changes made to the file's inode (such as changing permissions, etc). mtime refers to changes to the data within the file. So cnewer will use a reference files inode change time for the comparision, whereas newer will use a reference files data modification time.

Some manual pages are very vague and don't make a clear distinction, so your confusion is understandable!

FYI, there's also atime, which refers to file access time. Also, there is, unfortunately (and to the best of my knowledge), no way of finding file creation time through an inode.

Cheers
ZB