Categorizing spirits is always a messy business, and also one that is rarely entirely agreed on. Nonetheless I think its helpful to have some general idea of what qualifies something as a fairy versus something else, especially given how nuanced this subject is. The simplest answer is that when it comes to folklore, generally if the storyteller or person who experienced it calls it a fairy then its a fairy. However this gets complicated quickly because people experiencing fairies today are often doing so outside of the cultural framework the beliefs come from and this leads to some confusion, where a being is labelled a fairy because the person relating the experience doesn't have any other term available to them, whether or not 'fairy' actually seems to apply.
So what then makes something a fairy?
According to the dictionary a fairy is a mythic or folkloric being, human-like in appearance, with magic powers. This definition is not exactly either helpful or precise. If you really want to fully immerse in the subject I'd suggest Katherine Briggs' work or Henderson and Cowan's Scottish Fairy Belief, which tackle the twisting definitions across history and the general qualifications that might apply. Simon Young in his book 'The Boggart' also dives into this, and may be particularly of interest to those curious about the English folk belief side of things.
I'm going to give a short list of 'fairy' criteria, then dig a bit deeper into it. These 7 criteria are based on my own observations across decades of studying the subject, and I feel they do a decent job of differentiating a fairy from the wider range of general spirits.
1 Not an angel, demon, or ghost
2 Can have physicality/ interact in a tangible way with the human world and can also be incorporeal
3 Does not lie
4 Preference for dairy products
5 Come from and can travel to a different reality, aka the world of Fairy
7 May physically steal items/animals/people
There are other qualities but they overlap too much with other types of spirits to be useful. For example many (not all) fairies are averse to iron, but so are demons and ghosts in folklore. Fairies are sometimes said to interfere with electronic devices, but so do ghosts. Fairies have a kind of magic, called glamour, that can distort human perceptions, but there are other kinds of spirits that can also create illusions or mess with a human's perceptions of reality. So anything like that has been eliminated and the list focuses on things that are either unique to fairies or a hallmark characteristic found ubiquitously across folk belief.
2 Can have physicality/ interact in a tangible way with the human world and can also be incorporeal - one particular quality found of fairies across folk belief is the idea that they can be physical within the human world or can be insubstantial at their own will. Reverend Robert Kirk discusses this in his 1691 work 'The Secret Commonwealth of Elves, Fauns, and Fairies', describing the Good Folk as having bodies like condensed clouds, which the fairies can make appear or disappear. A German folk story related by Jabob Grimm in volume 4 of his Teutonic Mythology tells of an elf woman who entered a home through a knothole, like mist, then became physical enough to marry the man who lived there and give him 4 children before leaving again the way she'd entered.
3 Does not lie - one significant difference noted for fairies which is at odds with many other kinds of spirits is that fairies are reputed never to tell verbal lies. It is unclear exactly why this is, although Gerald of Wales writing in the 12th century claims fairies have no god but 'worship truth alone and hate falsehoods', so perhaps that is part of why (and also shows how old this idea is). Briggs explains this in her 'A Dictionary of Fairies saying, "Even bad fairies did not lie, they only equivocated.". Fairies can mislead a human easily with semantics and implied meanings, but they don't outright speak untruths.
4 Preference for dairy products - one thing that seems to be almost universally true is that fairies have a strong preference for dairy products across folk belief. Typically this means milk, cream, or butter. The Fairy Faith in Celtic Countries describes a practice of leaving both milk and butter for the fairies: "Whatever milk falls on the ground in milking a cow is taken by the fairies, for fairies need a little milk. Also, after churning, the knife which is run through the butter in drying it must not be scraped clean, for what sticks to it belongs to the fairies. Out of three pounds of butter, for example, an ounce or two would be left for the fairies.". This is one example out of many, but shows the idea of dairy being something fairies especially wanted. Many Irish folk stories discuss fairies stealing milk, even from cows in the field, and interfering with or taking butter.
5 Come from and can travel to a different reality, aka the world of Fairy - this one is perhaps a bit obvious, but worth mentioning nonetheless. The word fairy was originally a word used to describe a place, the land of Fairy, and the magic of that place, which was later applied to the beings thought to inhabit that world. These beings are believed to have an inborn ability to travel between their world and the human world, which they do for various reasons. Outside the English language speaking cultures in places like Ireland or Wales there were terms in those languages that conveyed a similar concept, a distinct world that these beings came from and could travel to.
6 Can profoundly impact human health/luck/finances - although fairies are not the only spirits who can impact human lives this way, doing so is one of their main characteristics across folk belief. On the positive side they can heal, give good luck, or bring wealth to a human they favour, while on the negative side they can cause illness, madness, death, bad luck, or financial ruin. If they are a fairy they can do these things, if they can't do these things they aren't a fairy.
7 May physically steal items/animals/people - a final criteria to note is that fairies have the ability - and are well known to do this - to physically take things or people they want. Whereas other spirits may be able to move an object the fairies will actually take it completely, so that it disappears often to reappear later in an entirely improbable or impossible place. Campbell describes this phenomena in his 'Superstitions of the Highlands And Islands of Scotland:
Additionally the fairies might steal an animal or a person rather than an object. Cows were regular targets of fairy theft, often seeming to sicken and die while they were believed to be taken into the fairy realm. In the same way humans might be outright taken, or might be replaced with a changeling which would obscure the theft. The belief was that the animal or human was literally taken out of the human world and into the world of Fairy.