Q:

What do we call all the humans?

In my world(s), there are many varieties of humans.  We have what we would think of as normal humans of various races and colours.  However, we also have other varieties of human, such as Satyrs and Fauns (ungulate legs and horns), Lamiae (a long snake-like tail instead of legs), Mermen (a cetacean or fish -like tail instead of legs, plus the more fish-like have gills), Lillim (with bat-like wings) and bird people (with bird-like wings), plus more.
Each of these races occurs in a number of different non-contiguous places, so they are not identifiable by their place of origin.
Each of these variants on humans have their own name, and can come with a variety of heritable skin colours similar to unmodified humans.  However, what would all these humans and human variants call what we would consider 'unmodified' humans?
They can't call them 'unmodified', since no-one really knows which came first or which has the greater population, and the concept of having been modified doesn't exist.
We can't call them 'normal', since typical members of each group would not be considered to be disabled either internally or externally, only differently-abled when compared with a member of another group, each having advantages and disadvantages in any given situation.
We can't even call them 'human', since they are all human, and are effectively the same species, able to interbreed, though as some crosses may result in less-fit offspring which are still fertile, they could be more accurately called subspecies of Homo sapiens.
So, what do they call what we would call 'normal' humans?

A:

They're all humans, then clearly you call them 'humans'. Humans on Earth all look pretty different, we call each one a human. I'm not sure where your aversion to this is coming from, but a human is called a human.
Certain breeds of dogs look even more different from each other than humans do, they are all still called dogs.
You're not looking for an alternate name to human, you're looking for the names of races. 

In biological classification, a race is an informal taxonomic rank, below the level of a species. It is used as a higher rank than strain, with several strains making up one race.

There are a few ways to divide races. There are physiological races, ecological races, geographic races, or chromosomal races. It sounds like you're going to have different ecotypes (ecological races), which you can refer to differently, but they are all still humans.

Ecotypes have no main taxonomic rank in modern biological classification. However some scientists consider them "taxonomically equivalent to subspecies". This is true in the sense that ecotypes can be sometimes classified as subspecies and the opposite.

Personally, I like the idea of calling them Morphs. Which, like ecotypes, can be thought of as precursory steps of potential speciation. Variations on this name can be used for naming. As a 'normal' arogant human I'd call myself a Protomorph, being the first of the Morphs. Others might say Amorph, being not-a-morph. 
There will likely be many variations on the names because they are informal. Some will be used in polite company while others will most certainly not.
You may need to know something or geography, the differentiation probably required some geographic separation, even if it's not that way now. Americans call seventh generation black american an 'african-american' despite them having no ties to Africa. Even if your humans are all mixed together, and they're apparently educated since they require politically correct names for each other, there have to be some prevailing theories as to where the groups originally developed.
If not that, then you can name them related to the animal they're closest too. We, the real-world human equivalents, would be most like primates, the bat wing humans like bats, etc.

A:

If They Are Another Species
But still in the Homo family, you can call them by their species' name: sapiens. Mermen could be formally called something like "Homo Serra." Fauns could be called "Homo Faunus." It would be a system that correctly identifies these creatures. (Yay Taxonomy!)
Call Them Descriptively
Alternatively, they could just call "normal" Homo Sapiens people leggies or footmen, or something that identifies them by their differences, just as we've done with races within Homo Sapiens. Despite some racial charges, you know what kind of person we're talking about when you say "white/black person." Likewise, if you are one of these "variant" humans, and you want to talk about the normal plantigrade humans, you can call identify them from the difference they have from you.
I focused on the plantigrade foot because it's the major difference between fauns, mermaids, and humans. Identifying them via feet would also work because it's the main method of (natural) locomotion, as your bat-people and feathered-people could use their wings (assuming they're capable of flight, of course). You could choose some other attribute, but this seems likely.
Everyone Has a Name For Everyone Else
If these creatures speak different languages, it would make sense that they would have different names for different groups. You see this is the world today. It's just a quirk of languages.
Everyone Attempts to Conform to a Common Name
... otherwise that group gets angry. It's like calling a person of color "black" in a real-life setting where people are very sensitive about that. Perhaps it could be like Brits calling Americans "colonists" even though everyone calls Americans "Americans". Americans can get fussy when you (as a Brit) call them colonists, so it is better to just call them Americans. This is confusing, though, because people from South America call themselves Americans as well, because they are from America, but not the USA.
Maybe I should have just chosen the Xiongnu, even though people call them and other unrelated people huns. I suppose the point is that a politically correct name for a group may or may not stick, despite people's best efforts. So your unmodified humans may want to be called "sapiens" or "entirely-skin-covered" but people call them "footies" or "locomotively ungifted" or something degrading like that.

A:

You could use "Humans" to mean any human, and "People" to mean anyone. If I read a story about animals, sometimes I might refer to them as "People" (even though they clearly are not) because they are the characters in the story. However, from my experience, "Human" always refers to someone of our species (unless you are a StackExchange-reading robot).
From the New Oxford American Dictionary:
Human:

of or characteristic of people as opposed to God or animals or machines, ...

People:

human beings in general or considered collectively...

So "Human" puts more emphasis on being an actual human, while "People" does not put as much.
TL;DR You could use "Human" to describe a person like in real life and "People" or "Person" to describe someone in any of your humanoid races. This is not the most "scientific" answer but probably fairly easy to catch on to while reading.

