What is the difference between the "wall flange" and the "flange less wall drain" versions. In what application would you use each?

The difference is the flanges on either side of the drain body. The wall flange drain is designed ideally to be installed wall to wall, and fit to the sheathing. You will use the flange-less drain body when you are going wall to curb or wall to curbless.

My tile is 10mm thick. Should I choose the 3/8" or 1/2" (3466 Wall recessed drain)?

You can choose the 3/8" style for a 10mm thick tile.

Drains Unlimited Wall Recessed Linear Drain

Name: Drains Unlimited Wall Recessed Linear Drain
Brand: Drains Unlimited
SKU: 3466-12 inch-No Flange-Stone
Price: 314.2 USD
Availability: InStock

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Drains Unlimited Wall Recessed Linear Floor Drain

Drains Unlimited Wall-Recessed Linear Drains are unique recessed drains that leave an invisible profile in any shower installation. DU Wall-Recessed Drains blend into their surroundings with a tile-in grate to match the wall tile. DUW Series drains can be applied to any single-plane slope shower installation.

Features

Available in flangeless (DUW) and wall flange (DUWR) models to fit with any size tile or stone installation
Made from heavy-duty 304 stainless steel
A passivated finish creates a food-grade, hygienic surface
It can be installed directly beneath a shower bench for a distinctive shower aesthetic
Magnetic, removable tile in-lay grate for easy cleaning and maintenance
Compatible with liquid and fabric waterproofing membranes
UPC, CSA, and ASME certified
Single slope pitch to drain
Easier to clean compared to conventional linear drains
10-Year Limited Product Warranty

Drains Unlimited