There are many words in existence I have seen or used to describe my size identity, here is a quick rundown. See the end for my experience with these terms.
Tiny (adj.)
Being physically small or diminutive in comparison to others. G/T tinies are named such because they are tiny.
Lilliputian as a media convention/trope
The Lilliputian is a specific being that usually resembles a human but tiny. Used in fantastical ancient and modern stories like Gulliver's Travels, and very closely linked to miniature Fae. Lilliputian stories often feature shrinking, regrowth, traversing the Mouse World, and on occasion, traversing the Human Body (See Innerspace, Fantastic Voyage). An umbrella label for the other words below.
The Tiny from the modern G/T community
A typically humanoid individual who is placed in opposition to a larger humanoid individual. Tinies may be explicitly nonhuman, paranormal, magical, or just human. Their size may be measured in inches compared to a normal human, or in feet compared to a megasized Giant. In this way, there isn't a size range to be a Tiny.
Tinies range from being presented as pest-like, to a discriminated underclass, to equal members of society. They can be strong representations for discrimination based on physical attributes. Tinies may also be associated with insects or small rodents, often experiencing primal instincts of fear as a prey individual.
The Borrower
A specific role or distinct species form of Tiny, which typically live hidden in Giant houses or gardens. They are generally unknown to Giants, seen as pests or mythical beings. They are known to keep away from larger folk, and take small items from them to live. Themes of self sufficiency and survival are important in Borrower stories. May be intertwined with legends of the Fae and folklore (e.g Brownies).
Regular humans may be forced to adopt the role of Borrower in certain stories. However in others, being a Borrower is distinct and marked by animalistic traits or superhuman abilities.
The Curious Borrower / Curious Tiny
A self coined label. A narrative position in giant/tiny literature. It depicts a Lilliputian who defies cultural norms in favour of their personal curiosity or drive to commune with giants. An example of such is Arietty, from the Ghibli movie, who defies Borrower law and befriends Sho, a human.