Kinda like wearing underwear with swim trunks, I get it.

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Which part is the airtight suit? Is that the white part ? I notice the green layer also has glove sealing rings.

I've been keeping track of Dava Newman's work on the MIT prototype BioSuit for the past several years, and spacesuit tech just keeps getting better and better. I think future suits will also be three layers: body stocking-type skinsuit layer, smart mechanical counterpressure layer with hard seals, and a coverall-type thing with radiation shielding, pockets, and so on. Snap on some gloves, boots, and a helmet and be good to go.

The helmet only attaches to the white garment. Also only the white garment has the hose connectors. But I wonder what's up with the rings on the green garment.

Pretty sure it's the green suit, although in the pictures I've seen, it's blue and looks slightly different. The white part is the Thermal Micrometeroid Garment - it's mainly for rejecting as much heat as possible and for protecting the airtight suit from pokey hazards (as well as micrometeoroids).