When ambergris is of a sufficiently high and excellent quality, (the finest really !). And has undergone the correct ageing process and transformation, during the many necessary years of floating and contact with sea and sunlight, for this transformation (chemical and biological) to occur correctly. And then (when out of the sea) it's aged even further to become well mature (the older it gets, the better it gets too !). It's scent profile keeps changing over the many years ... gradually losing most of it's more usual/common and brutally pungent "sea-skank-like" animalic/sea/salt/bile scent profile. All the notes mellowing, developing and maturing with time. If it is actually of sufficient quality and advanced age, it starts becoming sweeter and develops these distinct and intoxicating "ambery" notes. (As would a tincture of an excellent quality ambergris !) ...
(These were the really precious ambergris lumps, that kings would perfume themselves with. Proclaiming the most intoxicating and divine scent in the world ! ). ... (And , no, it did not smell merely of just animalic "sea and bile" like "skank". ~ As you would get from all other average quality ambergris). ...
And though, it never actually looses it's skanky animalic facets completely. It just becomes more well rounded, the skank much more subtle, warm, sweet ... and well ... with said marvellous amber-like scent !)

The chemical that ambergris produces which is mostly responsible for this sweet attractive amber-like scent is called "ambrein". "Ambrein" is the main active ingredient responsible for it's attractive and desirable amber-like scent. ... (And it is also this particular "ambrein" scent that perfume-labs try to replicate when reproducing new "ambergris" synthetic aromachemicals).
When ancient perfumers tried to replicate this sweet ambery note, with what they had at their disposal (i.e. just from nature). They found that the closest they could come to resembling it somewhat, was with a basic accord of Labdanum (most important !), Vanilla and Benzoin. ... (Labdanum alone is apparently the closest scent we have in nature, which comes anywhere close to resembling this renowned divine "sweet amber" scent of aged ambergris (and it's ambrein) ... Though of course you need the vanilla and benzoin for some warmth and sweetness etc. And most importantly of course, some skanky animalic notes for better accurate authenticity of the entire ambergris scent profile. ... It then begins to resemble it to a certain extent. Or, as close as we can possibly get.
However this is obviously quite difficult to reproduce entirely, and one will probably only ever achieve just "a close-ish very second-best resemblance" at very best ! ... (As it's scent too varies, apparently, from ambergris lump to ambergris lump, dependant on many various factors).
Then, to add more to the confusion : .... This is how the whole "amber accord" started out in "ancient" perfumery centuries ago. ... But meanwhile each perfumer since then has played around with this attractive accord. And each one, not knowing exactly the scent of the "original" (with very few ever possessing or even ever smelling "the real deal" probably ??? (As not all ambergris develops these sweet ambered scent qualities !). And with all also still being eager to further "add their own distinctive different touches and interpretation upon it", so as to differentiate their "amber perfume" from some or other "amber perfume" out there. Each will add their very own extra notes . ... And so, one might add more woody notes, whilst others more incense or spice, or a touch of this or the other. Just so they have their own slightly different character !?? (Lutens. for example, added much herbs to his "amber"

) ... And so on, and so forth ... !
So ... from just that basic base accord .... you still got many different smelling ambers.
So now, many many years later, you get many different ambers. And they'll all smell different (though also instantly recognisably "amber"). ... So much so, that it even became it's own "fragrance family". (And is also at the base of most, if not all, "Orientals" too !)
And when you get to amber synthetic aromachemical reproductions. Each company wants their very own ambergris/ambrein "smell-a-like" too. (And variants thereof ... like ambrox, an oxidation of ambrein) ... These are usually "copied" and derived from actual Ambrein (which is isolated from the Ambergris) ... Or they use (extract) ambrein-like products from Bee Balm or Labdanum (Cistus Ladaniferus) resin. Both have a scent which compares to ambrein, though their fixative qualities are unfortunately just not as good.
These synthetic "ambers" will also vary from company to company, picking up their own distinct scent profiles, signatures and variations. ... Though they all try to reproduce the ambery scent of ambergris/ambrein. ...
Which is why it is kinda difficult to tell you exactly what it smells like. For there are now sooo many different smelling amber notes, and amber accords. (Though, once you know how a few smell like, you should then be able to easily recognise all the rest, even when they're somewhat different .) ... There is very much a recognisable "signature", if you will.
Then ... To add still even a little further confusion : ... Once all these different ambers throughout the ages have been passed down and modified ... and then once again, ... and then once again, and so on and so on . ... You have perfumers copying copies of other copies that are already copies of other copies themselves. Which are by now copies and modifications of other copies etc. etc. etc. ... in a long chain of degraded modified ambers. Deviating more and more from the original intended scent.
This of itself has also gone on to breed another different type of amber scent. Lets call them "mongrel-ambers" for now. ... As these ambers are now actually no longer trying to replicate the ancient "ambergris/amber" ambers. ... That was kinda lost along the way somewhere !!?? .... And these now just try achieve a warm, resinous and very woody scent.
Of course here, because the scent no longer resembles actual amber, and more just a blend of woody resins. ... All sort of confusion has arisen as to the reason for naming them ambers. ... Is it from the Styrax resin tears (which also happen to look like "fossil resin amber") ... Or because Styrax resin itself is also from the tree named "Liquidamber Orientalis" ??? .... See, with all these different "ambers" left, right and centre (and I've not even mentioned them all yet !) ... It's not surprising there is sooooo much confusion about the name and it's origin. ... I mean, even because of this very confusion between "fossil resin amber" and "ambergris amber" , the French finally decided to add the word "Gris" (=Grey) to Ambre (which is what it was called before) , and the word "Jaune" (=Yellow) to the "fossilised resin ambers. ... And so we get AmbreGris (Grey Amber) = ... The source of our word Ambergris !
Though these resiny/woody accords and frags are still somewhat similar, because they still have many of the elements and ingredients of those past classical ambers. But usually just way more "pared down" and "simple". These are really much more about the resins and woods. And they've pretty much lost their "animalic" notes, and completely lost the "skanky" quality. ... They are much more woody and "cleaner", and really quite different. For these "woodier-ambers" are no longer trying to replicate anything to do with ambergris or ambrein in any way particularly. ...
The majority of these ambers are being made by Hindi essential oil and attar distillers and makers. ... And these are then mostly sold off to perfume manufacturers to actually use in the bases of their scents. Mostly for use in basic accords of their oriental bases. And they do have a vaguely "ambery" feel, though it's a different type of amber, being much more strongly about the resin-woody quality. ... (Though, don't get me wrong, a slightly woody quality was still part of the classic "ambergris amber" accords).
Sorry ! ... It's really not at all easy to explain. ... You will only truly learn the differences and then start understanding when you start smelling all the different ambers. ... Then their differences and similarities will all start making sense finally !
And on a slightly different Ambergris vein :
Now Ambergris has also always been revered for it's supposed excellent aphrodisiac qualities as well !
Here is an interesting article I found, that seems to perhaps proove that this may very well be true after all. ... Which I thought was very interesting and thought perhaps you guys might find it interesting as well !!??
http://www.ncbi.nlm.nih.gov/pubmed/8540767
That Ambrein might indeed be aphrodisiac !
And it'[s actually more these "types" of ambers that most people will probably associate with being an amber. (Rather than the more "accurate" skanky animalic ambergris/ambrein derived classic ambers).