I’ve covered a fair bit of taxonomy on here before, though there it lots more to come. However, I though it worth starting with synonymy since it’s pretty common in archosaur palaeontology and has led to a few misconceptions in the past. Synonymy is basically the practice of putting two or more names together as a single taxon because they are all the same thing but have multiple names.
This can happen occasionally when two parts of a single specimen have been named but of course it’s rare that two (or even one) people manage to split and animal in half and name different halves different things, though it does happen.
More common is that two different specimens have been described as two different genera or species but on closer examination they turn out to belong to the same taxon. This of course used to be pretty common since scientific communication was much slower and it could be years before you saw a paper by a colleague that showed that his new dinosaur was the same as yours (Cope and Marsh were especially good, or perhaps rather, bad, at this). Sometimes this is instantly obvious – both specimens are complete enough for an easy comparison and it’s obvious that there’s not enough evidence to consider them as separate species so they should be synonymised and brought together under a single name.
Now the more common situation is that two animals were named from two different but non-overlapping (or not overlapping enough) specimens. You might have a nice skull that’s diagnostically different to every other skull known so you reasonably think it’s a new species. In another formation a colleague has a new set of legs and a tail that look different to everything else known and names them too. Later on a third specimen turns up that’s nearly complete and it turns out that your skull sits on a skeleton that features a remarkably familiar tail and legs – you have both named the same animal and now it has two names. As an aside, this phenomenon is especially common in plant palaeontology where sometimes the leaves, twigs, trunk, bark, roots, flowers, seeds and fruit of a single taxon have all been named as different species at various times.
The resolution of this is, in theory, quite simple. Get a paper published that formally explains why the two specimens are both considered part of the same species and basically delete one of the names. The choice of which name goes if almost always down to the ‘principle of priority’, i.e. whichever name was published first is kept and the other one is demoted. This has been complicated in the modern age by the speed of publication and the appearance of advanced online publications and even online only publications which has required some changes to the rules as well as causing headaches (and the odd bit of acrimony) for taxonomists. It’s of course not always that simple as of course issues of ontogeny, variation and even age can play a role (if the two fossils are separated by 20 million years they’re unlikely to be from the same species even if they do look very similar).
There are exceptions to the principle of priority, but these are few and far between and easiest to skip for now though as a very brief example, ‘Brontosaurus’ was petitioned to be held over Apatosaurus on the basis that it was much more famous and would confuse or irritate the public. As you probably know by now, it lost out, though that hasn’t stopped the average reporter despite the fact that the formal synonymisation was formally put forward in 1903!
All of this causes confusion because it means that often names apparently vanish (like Brontosaurus, Aublysodon, and Laelaps) which can confuse people. Brontosaurus disappears from all the books, museum notices and TV shows (well, it *should* even today the damned thing still hangs around, but anyway) and people don’t realise where it went. Of course in a sense, it never went anywhere as in theory at least it’s a name that should not have existed in the first place. But since most of the public don’t realise how synonymy works (or even that it happens at all) they either don’t realise that the name is valid or assume that the old name / sign was a mistake rather than a formal change in the taxonomy (i.e. that the researchers screwed up and couldn’t tell their brontosaurs from their apatosaurs which of course is not exactly true and certainly not fair on the researchers. Oh alright, some researchers). That means that old names get re-used, annoying taxonomists and frustrating people who want to find out about say Antrodemus but can’t because books never seem to mention it anymore since it’s not valid.
Obviously the internet helps here a lot with sites often including old names so leaving a paper trail for people to follow but it is a problem and I once got trapped live on air on a radio show when asked about some taxon I’d never heard of and I didn’t know what it was. It turned out to be some obscure European sauropod whose name had lasted all of about 6 months before being synonymised but had clearly lived on somewhere long enough for a researcher to pull it up and the host ask me about it. Keeping up to date with the current taxonomy can be difficult (and of course there are disputed about names) but it’s very important to avoid confusion and the unwarranted multiplication of species.