Since you are using emacs... "info is your friend!"
The #<filename> files are the files which you are currently editing in emacs. They are recovery files. As soon as you save the file ^x^s or write the file ^x^w, they will go away.
If you quit the emacs editing session, with a kill or ^x^c, that is, without saving the buffer, these files will be left around as #<filename#> provinding a load for M-x-Recover to use. [part of the auto-save feature]
The tilde files (~) ARE backup files. They are created as soon as the open file is modified the FIRST time.
The behavior can be controlled via your .emacs initilization file.
Go to the emacs info system (^h^h i) move your cursor down (std emacs cursor movement keys work including search!) to the bold "emacs" entry and hit return, under files is "auto save".
(Navigate the info system with N/P/U (see top of info screen.)
About four screens down is "Saving files" navigate to "backup," hit return. Then "backup names. (note that version control is different from backup)
Note especially the section of Copying vs. Renaming.
The tilde form is on by default. It is changed via a "setq" statement in your .emacs.
Back on the main info menu about another 6 screens down is "customization" -- lots of info about .emacs in "Init file"
and futher down uner "Init File"
Most of the .emacs info is in the manual, not in info.
One thing to remember about emacs. Like Perl, emacs has more than one way to do things!