Levenstein (edit) distance is fundamentally an information-theoretical concept defined on bitstreams, as insertions/deletions/swaps of individual bits within a stream. It has a lot in common with error-correcting codes, fountain codes, and compression, which all also operate on bitstreams.
Any higher-level abstract mention of Levenstein distances (e.g. of Unicode codepoints) is properly supposed to be taken to refer to the Levenstein distance of a conventional (or explicitly specified) binary encoding of the two strings.
Any higher-level abstract mention of Levenstein distances (e.g. of Unicode codepoints) is properly supposed to be taken to refer to the Levenstein distance of a conventional (or explicitly specified) binary encoding of the two strings.