Yes, they are.
So this is probable for several reasons.
First, obviously the Naugrim are the dwarves — in this case the Dwarves of Belegost — and it’s called a dwarf-mask to signify that it’s made and used by dwarves. When used by the Naugrim it doesn’t need that signifier because it’s dwarves using them. So the different names make sense, and even support the idea of their being the same. Also, the Dwarves of Belegost were better friends of Elves than those of Nogrod — and delved Nargothrond, too — and so the idea of it being their masks that ended up in Nargothrond’s treasury makes more sense.
Secondly, both are identified as being awful and terrifying; the Valaquenta says of the Dwarves of Belegost that ‘it was their custom moreover to wear great masks in battle hideous to look upon’. Of Túrin it says that ‘he put it [the dwarf-mask] on before battle, and his enemies fled before his face’. So that fits.
Lastly, it says of both that it helped them against dragons: of the attack on Nargothrond by Glaurung and the orc-hordes it says that ‘none but Túrin defended by his dwarf-mask could withstand the approach of Glaurung’, and of the Nirnaeth Arnoediad it says that the Naugrim’s ‘great masks’ ‘stood them in good stead against the dragons’. Whether this was against their fire or their gaze, we don’t know, but presumably it was against their fire, since of the Naugrim it says that they ‘withstood fire more hardily than either Elves or Men, and it was their custom moreover to wear great masks in battle ... and those stood them in good stead against the dragons’, perhaps implying that the masks aided how they ‘withstood fire’.
But either way, the masks of the Dwarves of Belegost are probably of the same ‘make’ (if you will) of the dwarf-mask of Túrin.