What is the theoretical difference between probabilistic and embedding-based retrieval in NLP?

Probabilistic retrieval relies on term statistics while embedding-based retrieval uses semantic vector similarity.

Probabilistic retrieval (BM25, TF-IDF) models lexical overlap and term frequency distributions. Embedding-based retrieval encodes semantics into dense vector spaces and uses nearest neighbor search. The key theoretical difference is symbolic frequency modeling vs continuous representation learning. Hybrid systems combine both for robustness.