Proper way to repair old plasterboard walls?
That looks like plaster to me. They would typically (there are many variations on this... a pro-plasterer could be more definitive) apply what is called a brown coat over a substrate (maybe wood lath with scratch coat, maybe button-board, maybe gypsum board, maybe wire, etc.). The brown coat was cement mixed with a large proportion of sand. Then they would trowel on a finish coat of what you might think of as typical plaster.
You should be able to use whatever plaster material you want, including cutting out sections a installing gypsum board and feathering into existing wall sections. You could just skim-coat the entire wall with plaster (after addressing cracks/defects).The key is to properly prepare the surfaces prior.