A scan runs a rule across a known set. Every coin with real open interest, every strike in a chain, every ticker in an index. The set is defined in advance, the rule is applied to all of it, and the output is complete with respect to that set.
A search goes out and looks. It queries something it does not control — a news index, a social feed, the web — and returns what came back. The set is not defined in advance and the output is never complete.
Why the distinction matters
Both can return nothing, and the nothing means different things. A scan returning nothing is a measurement: the condition did not hold anywhere in the universe. A search returning nothing is an absence of evidence from one query, which is much weaker and often just means the phrasing was wrong.
A system that reports both as no results found has thrown away the difference, and a reader will generally assume the stronger of the two.
Coverage is a property of the scan
For a scan, the interesting question is what is in the universe. A screen across coins with liquid books is a different claim from a screen across everything listed anywhere, and a vendor that will not tell you which they run has not given you a number you can use.
Filters belong in the definition too. Excluding books below a size threshold is defensible and often correct; not saying so is not.
For a search, read the query
A search result is only as good as what was asked. A system that shows the queries it ran can be audited — you can see that it looked for one spelling of a name and missed another. One that shows only the results cannot.
The honest form for both is the same: say what was looked at, then say what was found.