A cat is an animal.
Cats are animals.
Do the two sentences mean exactly the same thing? If not, what are the differences and how do you use them?
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A cat is an animal.
Cats are animals.
The meaning of these two statements is, essentially, the same.
Of course, "a cat" is singular, and "cats" is plural. In most contexts, "a cat" would refer to just one cat. However, in the statement "a cat is an animal", a single cat is being used as an example that is representative of all cats, and that's why it means the same as the second statement.
It is quite common to use a single example as representative of the group to which they belong. A couple of well-known sayings about dogs are examples of this:
Although referring to "a dog" and "a man", this idiom suggests that all dogs are good companions for people.
This was a slogan from animal welfare groups in the UK to warn people against buying pets as Christmas presents, as many are abandoned soon after. Again, "a dog" represents all dogs.
Logically speaking they are equivalent. A cat is an animal if and only if cats are animals, so both sentences can be used interchangeably.
As you noticed yourself the difference is that grammatically speaking one is singular and the other is plural. This only matters if you combine the clause with another one and they have to agree on plurality. Take the following examples:
A. A cat is an animal and it needs to eat.
B. A cat is an animal and they need to eat.
C. Cats are animals and it needs to eat.
D. Cats are animals and they need to eat.
Here, the meaning of it and they changes depending on which clause is put in front.
In case A, the it means that cat (and implies it needs to eat because all animals need to eat).
In case B the they typically means animals (and given that the cat is an animal we can derive that the cat also needs to eat).
Case C is wrong. The it being singular wants to point to a specific singular "thing" in the first clause but there are only plurals in there so it doesn't really work, though nobody will have a problem understanding what you mean anyway.
In case D it's unclear whether the they points to the cats or animals in general (but both work so it doesn't really matter).
In most contexts "a cat" and "cats" have different meanings. "Cats" is plural and refers to multiple individuals.
In this particular context, the meanings of the two sentences are pretty much identical. You would use use the first if someone one asked you
What is a cat?
and the second if asked
What are cats?
And you would ask the first question if you were reading something and found the words "a cat" and didn't know what it meant, and the second if you found the word "cats".
It would be pretty rare to actually ask this about "cats" as that is a very common word. It would be rare to use those particular answers, since they don't really help define the word.
You can find examples on this site:
When we make general statements in English, we can frequently use either a singular or a plural subject.
If we use a singular subject, we interpret the subject as a representative or ideal of the class we're discussing. So in, “A cat is an animal,” the cat in question is some nonexistent ideal cat, having all the qualities of a cat and nothing that is not cat. So if that cat is an animal, all cats are animals.
If we use a plural subject, we're talking about the class itself. So in, “Cats are animals,” we're making a direct statement about all cats. Implicitly, we're saying, “All cats are animals.”
(Most English speakers hearing these sentences wouldn't consciously analyze them like this. They might not even notice which form was used. I just thought it might be helpful to see why the two sentences wind up meaning the same thing.)
Especially if the phrase is embedded in a larger sentence. For example,
The child knows that a cat is an animal, and it likes milk.
A bit unclear. Does the cat or the child like milk?
The child knows that a cat is an animal, and it, the cat, likes milk.
Awkward, but clearer. We're using an explicit appositive to make it clear we're referring to the cat. I might say this if I were speaking aloud and realized too late I was being ambiguous.
The child knows that cats are animals, and they like milk.”
Here “child” is singular and “cats” is plural, so it's easier to follow that cats also like milk, no explanation required.
That said, if it's clear enough from context who's who, you can usually use whichever style you prefer. Even in my example, it would probably be fine to use the first sentence — most people know that cats like milk, and it would be odd to give those two facts about the child as one sentence. The listener may just have to think a moment more.