Both SKUs have 350W power supplies, but they allocate the power differently:
The GPU-350W-TB3Z box has one 8-pin plus one 6-pin power connector. 300W is available to the GPU card and 15W Power Distribution to a laptop.
The GPU-350W-TB3 box is available only as the Developer Edition and has one 8-pin power connector, which is adequate to support the included Radeon RX 580 card. 225W is available to the GPU card and 60W Power Distribution to a laptop.
The numbers don't add to exactly 350W because power is allocated in discrete steps and some power margin is required for transients.
Note that some Thunderbolt 3 PC laptops with dedicated power connectors do not accept power distribution. To check whether your Thunderbolt 3 PC laptop accepts power distribution, check here. Upstream power continues to be provided even when the computer is sleeping.
Every Thunderbolt 3 Macbook Pro will accept Power Distribution, up to 60W for the 13" and up to
Thunderbolt 1 and Thunderbolt 2 computers will not accept Power Distribution.