Are these the same shoe?

Yes. The Tree Runner is one model sold in women's and men's sizing. The materials, midsole and insole are the same; only the size scale and color lineup differ.

Which is better for walking all day?

Both are equally suited. The SweetFoam midsole and light weight make either version comfortable for long walks, though neither has the support of a dedicated walking shoe.

They wear the same. The knit upper holds up well, but the outsole is thin, so heavy daily use on pavement will wear through it sooner than on a sturdier trainer.

Can I wear them without socks?

Yes. The Merino-blend lining is designed for sockless wear and resists odor better than synthetic linings.

Are they good for running or the gym?

No. They are a casual sneaker with a low-profile sole and no lateral support. Use them for walking, travel and everyday wear.

Should I size up or down?

Most owners find them true to size. The knit gives a little, so a snug initial fit loosens with wear.

Allbirds Women's Tree Runners vs Allbirds Men's Tree Runner

These are the same shoe. The Allbirds Tree Runner is sold in women's and men's sizing, and both listings describe the same TENCEL lyocell upper, SweetFoam midsole, Merino-blend lining and Featherbed insole. Buy whichever listing has your size in the color you want. Owners and reviewers consistently praise the breathable knit, light weight and sockless comfort, and consistently flag the thin outsole and limited wet-weather grip.

Choose the Women's Tree Runner if you wear a women's size and want the wider color choice that comes with the women's listing.
Choose the Men's Tree Runner if you wear a men's size, since the fit and construction are otherwise identical.

Prices

Allbirds Women's Tree Runners: $46.95 at eBay (last seen Oct 31)
Allbirds Men's Tree Runner: $46.95 at eBay (last seen Oct 31)
Difference: both cost the same at the latest prices (Oct 31)