If you have access to the query log, aka "who makes which query in what context"), you can use see which queries are "close" to others in context.

For example, with session, you can detect manual query rewriting, and use this as a signal to see which queries are close to others in the time context. You can do various fancy things from just that.

Nowadays, a simple way to start would be to use SOTA LLMs to generate synonyms offline, and use this for query expansion at query time. At least in a context where queries are small, that should give decent results. This has however diminishing returns because of cost (the more synonyms the more expensive querying the index), and also you lose precision with diminishing returns on increased recall.

Ofc, for complex search like google, I am sure it is much more complicated