The determiners, give a determination about a noun, and they give an information about a noun. They are used before the noun. They show the function of the noun. They show how the noun is used in a context. They show how that particular noun, is related to the rest of the text, and as such, are different from adjectives.
They do two things. The first thing is they identify things. The second is they quantify things, or show the number of things involved.
Determiners as IDENTIFIERS are giving more details about a noun.
For example, if you say ‘this car’, the determiner shows which car you are talking about. That determiner is called demonstrative, because it demonstrates something about a noun, ‘this car’. It identifies the car you are talking about.
Determiners can also play a possessive role. For example, when you say ‘my car’, it shows that you possess or own the car. This also is an identifying determiner, because it identifies which car.
When an article is used to show a specific thing, for example ‘the car’, it also is an identifying determiner, because it shows one specific car.
Determiners as QUANTIFIERS, show a number about things.
When a determiner is used as a quantifier, it shows how many things, you are talking about. For example, when you say ‘two cars’, it shows the number or the quantity of the cars, you are talking about.