Twitter messages have unique URLs (permalinks). It doesn't exactly have replies, though; you can send a message @someone (public, but intended especially for the given person) or send a private direct message, but there's no standard way to indicate which message you're replying to.
This is an intentional step back from email. Twitter is a bad place to have long back-and-forth conversations by design.
Twitter messages have unique IDs as well as an optional "message replied to id" (in_reply_to_status_id). The latter defaults to the last message from userX if you send a message with the @userX convention.
This is an intentional step back from email. Twitter is a bad place to have long back-and-forth conversations by design.