The primary difference between these two is that the Geometry > Alpha Mask pass displays the result of the masked geometry. So for instance, if you have a bunch of overlapping hair cards, you would see through the gaps between the hairs in this mode.
The Texture> Material Values > Transparency shows the raw material values, but not the result of the transparent effect. So in this case, you would see the full geometry and wouldn't be able to see between the gaps if one face overlapped another. This is useful for checking the texture content directly rather than previewing the transparent effect or creating a mask to compositing.
It's similar to say, viewing the result of specular lighting (not currently a render pass option in Toolbag, but I'm sure you've seen similar passes in other software), and viewing the specular texture map directly.
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The Texture> Material Values > Transparency shows the raw material values, but not the result of the transparent effect. So in this case, you would see the full geometry and wouldn't be able to see between the gaps if one face overlapped another. This is useful for checking the texture content directly rather than previewing the transparent effect or creating a mask to compositing.
It's similar to say, viewing the result of specular lighting (not currently a render pass option in Toolbag, but I'm sure you've seen similar passes in other software), and viewing the specular texture map directly.