A ref is anything pointing to a commit, for example, branches (heads), tags, and remote branches. You should see heads, remotes, and tags in your .git/refs directory, assuming you have all three types of refs in your repository.
refs/heads/0.58 specifies a branch named 0.58. If you don’t specify what namespace the ref is in, git will look in the default ones. This makes using only 0.58 conceivably ambiguous – you could have both a branch and a tag named 0.58.