Types of Magic

In the world of Hogwarts Reimagined, magic is a broad field with many avenues of use and learning. The terms witch, wizard and warlock are all gender-neutral as they have been throughout history, and refer instead to the way someone approaches learning magic. 
Most simply, this can be broken down as witch - nature, warlock - instinct, wizard - study. Every single magic user falls into one of these three categories, though they may also tend towards a subtype. 
Modern magical Britain favours wizarding most heavily, which sidelines many cultural practices that focus more on instinct or nature and many students struggle to learn magic the wizarding way. For example a warlock simply cannot perform spells the way a wizard does. They may very well be able to do the same spells and be just as good, but they don't learn them the same way. While a wizard thinks in terms of physics, mechanics and other sciences that go into each spell, a warlock works on instinct and an incantation if used at all is more of a shortcut or label than chosen for any scientific reasoning linked to its' exact function. Witches work differently again, by examining what is present in the environment around them and influencing the currents of magic already present, rather than by simply expelling their own magical influence. 
Squibs are not so much a fourth type as a subtype of magic user overall, and each Squib still falls into these categories of witch, wizard or warlock - though many may not know they do, as Squib capabilities for magic are not well-known and until recently Squibs were thought to be essentially the inverse of a muggle-born magic user. 
Most magic users cast spells, generating magic from a sort of internal well and expelling it to a wide variety of effects. The difference between Squibs and other magic-users is that Squibs do not have this theoretical magical well - they cannot produce new magic energy. However, they still have the fundamental fibres of magic in their being that allow them to interact with the innate magic in organisms and the world around them. Most magic users don't think of how much magic they simply leave floating around from the spells they cast, but a clever and well-trained Squib can twist, repurpose or even collect this ambient magic to suit their own needs. By nature of this, many Squibs are witches and closely attuned to the natural world by necessity, but it is still entirely possible for Squibs to be wizards or warlocks as other magic users are.
As other magic users may be, Squibs can be born to entirely nonmagical parents and go their whole lives not knowing of the magical world they inherently belong to. It is theorised that sometime after the Norman Invasion and the gradual prioritisation of certain kinds of magic, entire family lines of Squib mages became separated from the magical world and now their descendants may very well exist without any knowledge of their own magical capabilities.