Why does 'git merge' add files ending with tilde?

I’m in the process of merging two git branches that are fairly diverged.
After the automatic merge is complete, I ended up having multiple files having two versions:

file.cc~HEAD
file.cc~branchA

While the original file.cc was gone.
Since both files are identical, I’m slightly puzzled. Why does it happen? Which kind of conflict does it represent?

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