Is there a difference between the terms category and type? I can't seem to figure out when I should use one over the other.
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"Category" and "type" are largely synonymous with regards to their similar meanings. ("Type" obviously has a few other uses.)
The only real difference between the two is that a category feels more like a bucket or classification: Things are filed or stored away in categories. A type is more akin to a label or identification.
In both of these examples, you could not switch the words out for the other. This isn't so much a grammatical requirement; people just don't do it.
Also of note, the terms have become absorbed by Computer Science and Mathematics with very specific meanings and purposes. For more information, see the relevant Wikipedia pages for Type and Category.
A type can be a loosely defined collection, while a category is a sharply defined thing with a definite membership test. So he's the rude type, but he is in the rude category only if the rudeness distinction is sharp, so that you can test for rudeness. Sharp decisions are usually considered more arbitrary than loose assessments, because they require selecting a trait or feature and a dividing line.
So you can say he's in the tall category only if the "tall category" is defined by 6-feet and taller, and anything less is not "tall". If there is no dividing line, he's of the tall type. Consider also that something being of a "type" means only that it shares characteristics with the other things of this type:
The first suggests that he is Romanian, the second suggests that he is only sharing some vague characteristics with them.
Category conveys a grouping of similar objects. This is completely arbitrary in nature and one item can belong to many such categories.
While type tends to imply that an object can be identified by a particular attribute or trait. It strongly suggests that you should be able to classify it according to this particular attribute or trait that determines its "type".
An example might be that a book might be categorized into being a drama or a comedy or mystery in that it's entirely subjective. One person could interpret it as a drama while another could interpret it as a mystery. However, an example of a book's type would be fiction and nonfiction. This, unlike a category, isn't subjective and identifies what kind of book it is.
I'd say that a type refers to a group with common characteristics, while a category refers to a subgroup with a common set of characteristics and needs a clear supergroup in order to make sense. You are in a category, but you are of a specific type.
So, "He's the type of guy you can really trust", is correct, but "He's the category of guy..." is incorrect and "He's in the category of guys who..." is awkward.
On the other hand, "The next category of entries is bioluminescence", is correct, but, "The next type of entry is bioluminescence" is awkward at best. Similarly, "You're not my type" means "You're not the type of person I'm (romantically) looking for", while "You're not my category" could only be correct if you were in some kind of competition that was broken down into categories and added in ("You're not in my category").
When you have categories it can have different types. For example, "parts of speech" is a category which "pronouns" come under; and under "pronouns" you have different types.
Category fits to a family of different things, while type refers to the actual fact that something exists as being of this type.
Something has a type Something fits into a category.
Categories also are branched and hereditary, while types are just some qualification of an object.
Now you ask it, I can make this analogy: A directory describes a category you put things into. A label describe a quality of objects you put onto.
Now I make it more like computer sciences, put metaphysically, you put something IN a category, but you assign a type ON an object.
One is about the kind of object, the other is about the object itself.
BTW, types are more useful when you don't have time to find the good category. On the other hand, you can have a lot of labels, but you can't have too many different concurrent categories.
Other particularity of types, they can be mixed, while it's not possible with categories.
On the other hand categories make separation and organization easier: think of a (book) library or a hard drive partition.