Evolution is the way how the "mechanism" came to be, which is indeed very different. But the mechanism itself - spiking neurons and neurotransmitters on one hand vs matrix multiplications and nonlinear functions (both "inspired" by our understanding of neurons) don't seem so different, at least not on a fundamental level.

What is different for sure is the time dimension: Biological brains are continuous and persistent, while LLMs only "think" in the space between two tokens, and the entire state that is persisted is the context window.