Three lines that define search
A fun activity (within certain very narrow definitions of "fun") to play is to think about how many actions users need to take with different interfaces in order to find the information they want.
A quick and obvious answer might be that the minimum number of actions is two. There must be a search query and a click through to a result. One, two actions.
We can get that number down, though. If you've ever searched for something and had the answer at the top of the results (of course you have, this is 2024) then you've gotten what you wanted in one action: just the query. This, of course, is the same for well-tuned chat interfaces, too.
And how about zero? We can get there, too. Any kind of "push" information that is relevant at the right time is zero interaction. An example might be of an email alerting you that your credit card is expiring and giving you information on how to update it. Another example is from the long-abandoned Google Now. This was a set of widgets that would give you relevant information based on context such as the time or location. I remember being amazed when I landed in Italy early in the morning that the home screen of my phone had a card with how to say "good morning" in Italian as well as the USD to EUR exchange rate.
The opposite holds true as well, in that we can also imagine situations where the number of actions is much higher. Irrelevant search results are likely to lead a high number of user interactions, but I'd propose that the number of interactions can be effectively infinite, and that isn't necessarily a bad thing.
Recommendations take user actions and build an understanding of what a give user (or cohort of users) would want at a given time. Indeed, those recommendations should get better over time, as users perform more actions. So, the level of actions before a successful result is boundless.
Thus, our first line that helps us understand search is that between zero and infinite actions before success.
Another useful way to think about how users get to something worthwhile is through the opposing lens of finding and discovery.
Finding is all about the user having an item in mind and getting to it precisely. Discovery is all about users coming across items they didn't know they wanted until they saw it.
Finding generally will come through search, where a user is explicitly providing an intent. When a user searches for "black and white checkered" on the Vans website, the goal is to find a specific product.
Discovery is more often found on (e-commerce) homepages and category pages. These pages have a weak intent signal, and so instead are an opportunity to present the user with options and inspiration.
A third way to think about offering up results is through precision and recall. Precision is when the only results that are shown definitely relevant, even if some relevant results aren't shown. Recall is when all relevant results are shown, even if some irrelevant ones poke through.
A SQL query is going to be precise. The only results that come back are the ones that exactly match the query.
SELECT * FROM products WHERE product_name = 'Everywhere Belt Bag 1L';
Keyword-based search also leans toward precision. There are query relaxation techniques that move keyword-based search further along the line to recall, but generally a result is in the result set because it matches the query word, and it's not if it doesn't.
An extreme example of recall would be something like Pinterest. A bunch of photos laid out for you, ready to inspire. The users generally don't have one single photo in mind when visiting Pinterest but want to discover something around a theme. (This shows well how precision and recall are closely related to finding and discovery.)
Increasingly search engines have started integrating vector search as well. Vector search tends to correlate with recall over precision, as results are generally selected as nearest neighbors to the query, so you are more likely to get a relevant result while you're also more likely to get some irrelevant results.
(This is also why many search engines are opting instead for a hybrid setup, with both vector and keyword retrieval, as they try to balance the precision and recall from the two systems.)
No one position on these three lines is right or wrong. They are instead right or wrong for a given context, and they can help you think about the experience that you're trying to offer to users of your site based on what the users are trying to achieve.