A subspace weapon is any device that utilizes subspace in a primary role. That is, like the warp drive, it generates a subspace field to produce whatever the effects of the weapon are. A phaser, on the otherhand, only has secondary subspace effects. While it shunts matter into subspace, and possibly pulls energy out of it, it doesn't utilize subspace itself to do this.
In other words, a subspace weapon "pulls" subspace into normal space, while a phaser only utilizes energies present in normal space to produce subspace effects. That is, a phaser manipulates an object to push it into subspace, while a subspace weapon manipulates subspace itself. (For more on how I'm picturing subspace, I'd direct you to Paul Cargile's theories regarding the subject, but they don't appear to be online quite yet.)
Subspace weapons are banned because, unlike phasers, they have the ability to change the nature of subspace in the area they are used, and therefore may cause damage to the very fabric of spacetime.
I guess that's a little less clear then I'd like it to be.
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"I'll turn everything around and confuse you. I'll fix it so you can't remember what was true."
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They Might Be Giants
(Sol, I was waiting on a second return email from you which is why I didn't post the subspace theories before. . .)
But now I have the whole thing that I and Baloo brainstormed on, with three pictures right HERE.
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I'm the only one who understands me, and I ire of my company.
--Paul Cargile
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"I'll turn everything around and confuse you. I'll fix it so you can't remember what was true."
--
They Might Be Giants
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The best thing about being a solipsist is that I'm the only one here.
--Paul Cargile
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"The record of my unspeakable crimes, in previous lives, in previous times, indelibly stains the pages of history."
--
They Might Be Giants