So the "Squareness Gun" that River has is actually Jack's sonic blaster but she calls it a Squareness Gun because she doesn't know what it is? It's just /set/ on the squareness setting that he had it on last, he left it in the TARDIS and we assume that River took it at some point while on the TARDIS and used it in Silence in the Library. Woah :)
That’s what Rose called it too. :D I was under the impression that it made that square pattern (vs a circle) because it was digital.
Anywho- yeah, it’s meant to be the same gun. In one of the Comics, the Tenth Doctor tells a companion she can’t take it because it’s reserved for someone else.