I've written already about natural ambergris (also called Ambra) and mentioned there that most perfumery uses synthetic substitutes.
Here I'm setting out some of those substitutes (mainly synthetic, but including some naturals) and trying to sort out some of the confusion resulting from the fact that there are so many different products with very similar names.
The the ambreine produced from labdanum that Aftelier sell is a proprietary product of Firmenich ('one company in the world' reference is a very romantic way of saying that one of the three dominant players in the perfumery ingredients market makes it and has kept the process a secret). I'm not quite sure whether that's the same as the Ambrain also produced by Firmenich but it seems very likely that these are two names used for the same product.
Another similar product is Ambrarome which was originally made as a replacement for natural ambergris and is also made from extracts of cistus. I use ambrarome in my work when I'm looking for a distinctly animalic note.
Ambrox is a term usually used to mean Ambrox DL or one of it's synonyms: quite different from the labdanum based materials because it's a brand name for a single synthetic molecule (though a mixture of isomers) which replicates one of the components of natural ambergris. The term ambrox is sometimes used to mean any of a range of similar products, in particular Ambroxan / Ambrofix / Orcanox that are brand names for chiral isomers, which though similar, are not quite the same. In my work I mainly use Ambrofix, which is made by Givaudan from a natural starting material, though I do use some of the others too.
Just to confuse matters further there is also Ambrein which is the waxy substance that is the majority component of natural ambergris, the breakdown products of which give the precious scented molecules of ambroxide and others that have been replicated by the various brand-named products above. When pure, ambrein is odourless. Bo Jensen provides a good description of what's going on (scroll down to the text just below the whale pictures). I also use several of the other substitutes mentioned by Bo Jensen in his article for particular purposes.
Further confusion often arises between Ambergris (Ambra) products and Amber - a term that in perfumery is sometimes used to refer to a product made from the fossil amber by destructive distillation of the waste and low-grade amber left over form the jewellery trade. This is described by Arctander as having a "smoky, tarlike, resinous" odour "with a distinct resemblance to the smell of tanned leather". He mentions that there is also a rectified version of this oil, which has been steam distilled as well, but this is very little used in perfumery.
More often however amber refers to a blend of ingredients intended to give an warm scent reminiscent of both ambergris and the appearance of fossil amber (which in its raw state has virtually no odour). Such blends normally include labdanum, vanilla, benzoin and other ingredients are are often used as fixatives. Some of the products named in the first paragraph fall into this category, but many perfumery houses and others will have their own blend.