Fake Blythe dolls, also known sometimes as Blyth or Blybe or tbl (short for Taobao Blythe), have became very popular in recent years.
Background[]
Originally unofficial Blythe dolls were sold and marketed as "Factory Blythes" from the unproven theory that they were made from displaced or substandard official manufacturer's pieces. This term "factory" is still used by collectors today as a synonym for "fake." Today many of the manufacturers of these dolls have made their own unique face molds that are no longer cast from official Takara releases.
Fake Blythe dolls are especially attractive to customizers as they are much less cost prohibitive than official stock Neo Blythes. Within the past ten years or so it has become a standard offering to include a recast jointed body modeled on the Azone PureNeemo XS, enabling new customizers and collectors to have superior pose-ability without the expense, risk, or hassle of re-bodying an expensive Stock doll. Fake Blythe dolls also have a wide variety of hair colors and styles and an array of skin tones making them attractive to collectors and customizers alike.
Blyth[]

Two Blyth dolls with different face molds, both produced by DBS
The most common fake Blythe doll offered is labeled as the Blyth doll. This doll comes on a sturdy recast Azone body. Most often its stock eye colors are light pink, grey, a purple cast blue, and a orange cast brown, but many sellers will caution the eye colors are random. There are numerous face molds offered as "Blyth" dolls on marketplaces like AliExpress, Alibaba, Wish, and originally on Taobao. Most of these dolls are manufactured by an entity known as DBS. In addition to the various face molds, Blyth dolls are offered in both shiny and matte versions and feature six skintones: white, fair, normal, tan, dark skin, and black.
Icy[]

A 2009 Arker Icy "Big Eyes, Big Head" doll
Icy Mold by Arker[]
The Icy doll was originally a mold created by a now defunct manufacturer called Arker, but in recent years the mold is sold as a recast within the Blyth continuum offered by DBS. The original mold was inspired by Blythe doll, described as a "Big Eyes, Big Head" doll and came on a Takara Licca body. They have a distinctive look, with a wider and longer face, almond shaped eyes, and a very thin mouth. Icy dolls also have slightly smaller eyechips than a standard Blythe or Blyth doll.
Use of the Term "ICY" in Marketing[]
In recent years, the term ICY has been used for marketing purposes which can be confusing to new collectors. This practice originated as a way to ensure someone looking for an "Icy" doll would return many related results in the SEO. This practice has become so wide-spread that some sellers even include the word "Icy" on their packaging. Icy is not a company, manufacturer, or a brand of dolls. It is a marketing term that originated at the time of the Arker dolls becoming desirable to collectors.
Basaak[]

Basaak dolls
The Basaak Blythe is a budget offering featuring a unique face mold and body. The body does not have articulated joints but it does have heeled feet that are able to wear vintage Barbie doll shoes. Basaak dolls are sold at very low prices, usually below $10 USD, and so they are not manufactured in a way that makes them a reliable base for customs. The eye mechanism is brittle. Basaak dolls have distinctive eye chip colors compared to more common factory Blyth dolls and also have bright red lipstick and shiny faces.
NBL or New Blythe[]

An NBL doll
NBL or New Blythe doll is an iteration of the imitation Blythe doll found mostly on Amazon. The NBL doll has a couple of face molds and a unique jointed body that is shiny. This is another budget offering where the bodies are very fragile and prone to break, making it unsuitable for customization.