It looks like the customizable variant of the P1 Gen 2 has different GPU options (including iGPU-only) based on what processor you choose, while the X1 Extreme Gen 2 has a Geforce 1650 in all configurations.

If I had known that when I was picking out an X1 for work, I would have pushed a P1 with no dedicated GPU instead.

The 14" X1 Carbon does indeed come with Intel integrated graphics, but I was specifically referring to the 15" X1 Extreme.

(Also, what pentium166 says.)