In a local shop they built a huge Russian type hut out of wood and carpet, but I cant remember the name of it.
Probably a Siberian 'chum'. Looks kind of like a tipi.
There's more kinds of shelters than you could possibly name - and most have 'sub' catagories and variations. And lots of people call the same design by different names.
There's the aframe - the 'debris' shelter, all kinds of 'trench' shelters for snow and dirt, there's quiggly holes, there's log cabins and structures, there's tipi's, yurts, chums, etc, there's so many that it defies cataloging.
Instead - look at the design elements, and then look at the "roof" materials. That generally will narrow it down a little and most structures are comprised of a handful of basic designs. It basically boils down to single slope roof, double sloped roof, conical and flat, and materials are natural or man made, and fall into 'debris', wood, soft (like tarps) or hard. Then you add 'enclosed or exposed' depending if it completely shelters or has a permanent opening that's part of the design.
A 'lean to' is a single sloped roof with no sidewall (roof goes to the ground) using a high angle with an exposed front. It might be made of natural wood and debris (such as leaves and moss) or it might be man made such as a tarp.
An a-frame is a double sloped roof (slope on each side) with no sidewall that may or may not be enclosed or exposed at the ends. May be hard or soft walled and made with natural mat's and debris or man made such as a tarp.
A tipi is a conical or point roof with no sidewalls, usually made of man made or processed soft materials (such as hide, tarp, etc).
There are massive numbers of variations on the themes.