Is there a difference between the investigation letter issued by the law firm and the court transfer letter? What if the unit doesn't turn?

Of course there is a difference. The court belongs to the national judicial organ. When the court investigates, the person or unit under investigation must cooperate unconditionally. Failure to cooperate will constitute obstruction of litigation and the court can punish it. The law firm is an intermediary institution, and the respondent or unit has the right not to cooperate with the lawyer's investigation. If the respondent does not cooperate, the lawyer has no right to punish the respondent and can only apply to the court for investigation.