Custom fields are a database structure originally built for plugins to store meta data associated with various things, including users. Originally the only way to create/update them was via a plugin.
Later we added that custom field admin section to make it easier for discourse admins to add forms and capture certain values. It uses the same back end as the plugin system, but you need to use the database name to access them.
It might be a good idea to accept either name, now that you mention it. I doubt there would be a conflict if we searched by name first and if not then value.