The overall structure is the same as in "use statistics to predict the next token."

With a Markov chain, the statistics are as simple as a mapping of n-grams to the number of times it appears in the corpus.

With a LLM, the statistics are the result of 50 years of research in neural network architectures, terabytes of training data, and many millions of dollars worth of hardware, along with the teams to build and manage all the data pipelines.

So yes, much more complicated.