Several answers touch on this already. “Intelligence” is a very flattering “magic” feeling that doesn’t really explain what is happening with LLMs.

Probablistic/Statistical weights are heavily involved here. But it feels “intelligent” because of a combination with ever-expanding processing/computational speed and power that can be thrown at the prompts. Things that were previously limited to on-site super computers can now be accessed via the internets/online services.

It’s worth noting also that dynamic “seeding”, such as via on-demand searches can contribute to better/worse context resolution.

AI is the common speak for large language model querying (with all the above, plus other details), in mind. So, Probablistic Inferencing (at) Super Speed (i.e. “PISS”) seems about right to me!