So if I understood correctly at first we need to create an embedding and then is it directly inserted to database? or at first it should be indexed? or a first it is indexed and only after that stored in database
I'm just trying to figure out the process for exaplaining it in my essay
Yes, that's correct understanding. A developer shouldn't need to worry about the indexing part of a database that offers the vector search capability and only do the ingestion with the appropriate embeddings. The index building process happens at the database level and each database does the indexing in its own fashion. For e.g. some databases gives immediacy while some does asynchronous indexing which takes time to catch up the indexes to be able to serve the fully relevant data. See this report that talks about how hard vector search problems were solved for.
Where the developer needs to worry is that if the indices for the data that was just inserted isn't available at the read-size immediately (i.e. real-time) and giving poor relevancy/throughput/latency until it catches up and completes fully indexing.