pg_vectorize is a wrapper around pgvector. In addition to what pgvector provides, vectorize provides hooks into many methods to generate your embeddings, implements several methods for keeping embeddings updated as your data grows or changes, etc. It also handles the transformation of your search query for you.
For example, it creates the index for you, create cron job to keep embeddings updated (or triggers if thats what you prefer), handles inserts/upserts as new data hits the table or existing data is updated. When you search for "products for mobile electronic devices", that needs to be transformed to embeddings, then the vector similarity search needs to happen -- this is what the project abstracts.
There's an API that abstracts vector search only. vectorize.search() and that part is not unique to LLMs but it does require selection of an embedding model. Some people have called embedding models LLMs.
vectorize.rag() requires selection of a chat completion model. Thats more specific to LLM than vector search IMO.