Some of these GPT engines maintain their own vector DB to do semantic search, others are directly hooked into Bing / Google. So pubmedisearch.com would be one component of a GPT-based engine. We actually have a GPT-based engine here: https://medisearch.io/.
Glad you like it! I did this as a mini-project within our startup MediSearch (https://medisearch.io/) & the search pipeline is custom tuned for the problem.
It uses a vector search approach. Your query is embedded in a vector space using a language model and we find the closest vector to the query from the PubMed papers. This is a good summary of the techniques: https://learn.microsoft.com/en-us/azure/search/vector-search.... There are a couple more tricks but this is the gist.
The nice part is that this approach allows you to find relevant papers to your question. E.g, you can ask "Can secondhand smoke cause AMD?" and the very first few papers are answering your question (https://pubmedisearch.com/share/Can%20secondhand%20smoke%20c...). The more specific question, the better. :)