Is vector store actually an OpenAi api-only, internal vector database?

In order to store files in OpenAI, I need to make a vector store:

https://platform.openai.com/docs/api-reference/vector-stores/create

And use file_search module, in order to create assistant:
https://platform.openai.com/docs/api-reference/assistants/createAssistant

But is vector store actually a Vector DB only for OpenAI api calls?

You are correct, it can only be used by the file_search tool within assistants, when the AI calls that tool.

The first GB of persistent vectorDB storage is free per day, along with free file uploads to storage, with no cost to perform document extraction and embeddings model AI calls on the chunks when storing.

The profit is realized by the AI employing the tool and generating based on 15000 tokens dumped into the model input context. Not by OpenAI being a database provider.