I had to deal with typographically printed sheets with some generic text and fields to fill in information by hand (dates, signatures etc.) or through printing (if you are lucky to hit the fields). Each sheet has a watermark, its own serial number, and is unique.
Literally translated from Russian they are called “forms of strict reporting”, but I would like to know what a native English speaker calls them.
I am unaware of a special English term corresponding to that description. We would call such a thing simply a “form” or a “fill-in form”. If it had some special bureaucratic significance it could be an “official form” or a “standard form”.