Describe the difference between A and B. There is one difference, describe it.
Describe a difference between A and B. There may be more differences, describe only one of them.
Describe the differences between A and B. There are several differences, describe them all.
Describe differences between A and B. There are several differences, describe some of them.
Describe difference between A and B. Wrong indeed
As J.R. remarks, there is some room for interpretation in the third sentence. The writer might not expect the answerer to give all the differences, but that depends on the situation.
If I ask a general open question about a subject the student should have studied, I could ask:
What are the differences between a monarchy and a republic?
I would expect you to answer the main distinctive differences about the forms of government, and not, for instance, whether during the 3rd century ad in western South America, societies resembled a monarchy more often than a republic.
However, if I gave you a text to read and I ask you
What are the difference that the author has noticed between the red and the blue phone?
I do expect you to list all the differences that are mentioned in the text.
In general, when you use the definite article (the), you indicate that you want a description of the specific thing or things you are asking about. So not just some random difference, but the difference, the one difference that exists between A and B - or the differences, the whole set of differences, all of them.
When you use the indefinite article (a or zero, no article), you are asking to describe any difference, or differences, that apply to A and B, but not the whole set of differences that might exist.
There is a little but in this:
When someone refers to the difference between A and B, it usually does not imply there is only one difference!
The difference, often with the emphasized in some way, spoken or written, means the most important difference.
Suppose I write an article about two new phones that come out. They have slightly different prices, they have a slightly different performance and the other one lasts half an hour longer on the battery.
But the difference between phone A and B is the screen: A has a 2 inch VGA-resolution screen, whereas B sports a state-of-the-art 42 inch WTFBBQXSVGA-resolution screen.
a variety of flowers
This refers to a set which contains several kinds of flowers.
Ex. "The bouquet was made up of a variety of red flowers." (They're all red and part of one set, but are different from each other in terms of genus, species, cultivar, and so on.)
varieties of flowers
This refers to multiple sets, each set containing many instances of one kind of flower.
Ex. "Several varieties of flowers are available for purchase." (A flower shop offers several different kinds of flowers, and they sell more than one of each.)
a variety of flower
This refers to a subset within the set of the whole, as in one kind of flower among all kinds of flower.
Ex. "A variety of flower may hold they key to curing cancer." (One particular kind of flower contains compounds that have some effect against cancer, but flowers in general do not have such properties.)
varieties of flower
This refers to several distinct subsets within the set of the whole. Ex. "Several varieties of flowers bloom all year round." (There are several kinds of flower that blossom throughout the year, but there are also those that do not.)
Best Answer
Before I get to the sentences and their meaning, first a short note about there're.
It is used as a contraction, but not very commonly. It is perfectly fine to contract are to 're, but for pronunciation reasons this usually only happens after a vowel sound: they're, you're. The r sound at the end of there makes it more difficult to pronounce for most people, so most will prefer to use there are.
Now, for the sentences. There is an obvious difference between these two:
The first one is singular, the second one is plural. However, because there is a negation, the result is the same: there are zero cars. So as such, the two sentences both mean the same. They are also both grammatical.
Another way to say the same is using any, and the correct way of doing that (again singular and plural are correct!) would be:
You could say there are not any cars, but the contraction feels more natural.
Now, if we have four ways to say the same thing, which one do we choose?
Actually, the difference between the four options is quiet small, but there is a little bit of difference in how we feel part of the message is stressed.
If we are talking about a single car, say a car that I have reserved at a car rental, but they messed up my reservation, you could have a conversation like this:
Let's have a look at the messages behind the four phrases in this conversation:
There is no car: you expected a specific, singular car to be there, but it is not there.
There isn't any car: not only the specific car you wanted isn't there, there is no other single car for you.
There are no cars: I would expect there to be several cars, but that is not the case.
There aren't any cars: Really, no matter what kind of car you want, there are none!
Although there is a bit of a difference, most speakers would have no problem interchanging at least some of the options in the conversation. In general, adding any will add some stress to the absence.