Ah, you’re lucky geology is a favorite minor hobby of mine. :) Nope, sorry, obsidian is a distinct material. It’s a volcanic glass, more than ¾ silica, and can be recognized by its translucency, its brittleness, and the way it fractures.
Which is why obsidian is suitable for knives and arrowheads, because of how sharp the edges can get. In fact, the obsidian we use in our world can get beyond super-sharp – with an edge as thin as a millionth of a centimeter, an obsidian scalpel can cut individual cells in half, making ordinary steel scalpels look like chainsaws. More info on this here.
In comparison, the black stone is “fused stone”, harder and evidently suitable for building. (The Black Wall of Volantis,
Dragonstone castle,
the base of the Hightower, the Five Forts, etc. Note I believe that the black stone that makes up the Seastone Chair and Yeen and the idol on the Isle of Toads may have a different origin.)
No mention is made of it having brittleness, nor translucency. And since the books mention basalt and granite and jet and coal and marble and onyx, that means the maesters know how to identify those particular black minerals, and so the black stone can’t be any of those. Well… it can’t be any of those minerals anymore, that is.
The dragonlords of Valryia, as is well-known, possessed the art of turning stone to liquid with dragonflame, shaping it as they would, then fusing it harder than iron, steel, or granite. –TWOIAF
Stone does not burn, Harren had boasted, but his castle was not made of stone alone. Wood and wool, hemp and straw, bread and salted beef and grain, all took fire. […] And even stone will crack and melt if a fire is hot enough. The riverlords outside the castle walls said later that the towers of Harrenhal glowed red against the night, like five great candles… and like candles, they began to twist and melt, as runnels of molten stone ran down their sides.
–TWOIAF
The black stone that the Valyrians created is apparently made by some process similar to how Harrenhal was (half-)destroyed. The stone is heated by dragonfire until it becomes liquid, then when it cools it’s fused (somehow, I suspect with magic) to become super-hard. This process could probably work with any quality building stone; but as an example, in our world there’s such a thing as fused cast basalt:
Pretty neat, huh? Very hard, wear-resistant, black, shiny – and the shaped pieces are almost oily-looking, wouldn’t you say? It’s made by crushing basalt stone and smelting it at 1250°C
(2282°F). And interestingly, dragonfire has been estimated to be about 2300-2800°F.
Also, while in ASOIAF obsidian is called dragonglass, it is known that
it’s formed as the result of volcanic activity, not dragons. The
volcanic island of Dragonstone is a great source of obsidian; but it’s
not the only place where obsidian can likely be found, as the hot
springs of Winterfell reveal geothermal activity there. (The Children
of the Forest’s caves further suggest they may have sought deep into the
earth for obsidian for their weapons.) Mind you, GRRM says in his world obsidian has magical characteristics,
so indeed there might be some connection to dragons – I mean, the
Valyrian name for obsidian translates to “frozen fire”, which is
definitely significant considering the title of the series – but it may
be a connection in the same way that dragons were supposedly originally
found nesting in Valyria’s volcanoes, the Fourteen Flames.
So, in ASOIAF, both obsidian and the fused black stone are magic in some way – in the black stone’s origin, and in the properties of dragonglass (especially in how it can kill Others) – and yet they are distinctly different materials. Hope this helps you see the difference!