A search is one counterparty checked against every source in the plan. You look up a person or a company and the platform returns a consolidated result with what each source contributed. You are not charged one search per source reviewed: crossing all of them is what makes up the search.
Monitoring is a separate service: it keeps watch over counterparties you have already screened and alerts you when a new match appears. It does not draw on your balance of searches and is contracted separately.
The exact consumption terms — what counts as a re-check, and within what period — follow the service you contract. If your operation hinges on a particular case, confirm it before buying: we would rather clear it up now than argue about it later.