In the generative AI world, zero shot learning is when you write a prompt and get a response. One-shot and K-shot are more similar to writing a prompt that includes one or more example completions for the model to learn from. Fine tuning, where you take the existing model and train it off a dataset specific to your query, is a type of k-shot learning.
For more on these techniques, check out the Large Language Models for marketers in the BrXndscape.