When you select the tag zero-shot-classification in the model hub (see here) you can see all the models for the task. The default in the pipeline is facebook/bart-large-mnli (see source code here)
Hugging Face’s zero-shot classification is always based on models pre-trained on Natural Language Inference datasets (like mnli). So under the hood, it’s actually doing an NLI classification, it’s just abstracting that part away for you (see details and further links here)