Some people contend that using the term loli to describe a character always implies a sexual attraction on the part of the person using the term, which is vigorously denied by those that use it. There are some that claim that a character's given age can exempt them from loli status (for example, the character Konata from Lucky Star, who is 18 years old but also an extremely late developer such that she appears to be roughly eleven or twelve); others generally hold that these people are merely trying to justify their attraction to such a character without admitting they are paedophiles, since there doesn't appear to be any other reason to try and make this distinction.
Related to this is the slang weeaboo term "moe" (pronounced "MOH-eh"), which literally means "(plant) budding," and a pun on "burning" with passion or light or life. Started out as a way to describe girl characters that were between the ages of Yotsuba and SailorMoon, these days it's either used by fools with white-knight syndrome to describe girls that are so young and cute you want to take care of them, or used by filthy pedos to make you think they are one of the fools with white-knight syndrome.
The rule 63 version of Loli is Shota, which is typically preferred by either overly maternalistic women or very, very creepy men.