Split each term in two. "Positive" or "negative" is what the tool said: it alerted, or it did not. "True" or "false" is whether the tool was right. A false negative is therefore a quiet tool that was wrong. Translating each option into "tool said / reality was" settles most wording traps in a few seconds.
In vulnerability scans
False positives come from detection by inference. A scanner that cannot log in guesses from what a service announces, and a check written for one product version can fire on a host where the vulnerable feature is installed but switched off. A credentialed scan removes much of that guessing.
False negatives come from what the scanner never reached: a laptop that was off during the scan window, a segment the scanner cannot route to, or a flaw too new for the scanner to have a check. A rescan after a fix (objective 2.3 calls it validation of remediation) is one of the places a supposedly closed finding turns out to still be open.
In SIEM and detection rules
A rule that matches an administrator's scheduled maintenance script will fire every night: a false positive. A log source that quietly stopped forwarding produces the opposite. The rule is fine, but it never sees the events, so it can never fire.
Tuning moves errors between the two columns. Tighter thresholds and broad suppressions cut false positives and raise the risk of false negatives; looser ones do the reverse. Objective 4.2 asks you to report both rates for that reason, and the automation and process improvement guide covers rule tuning as a standing task.
Which error the exam treats as worse
Asked which error is more dangerous, CySA+ wants the false negative: a missed intrusion keeps running while the queue looks calm, and the time until someone notices is what the mean time to detect metric measures. A stem that describes analysts skimming past alerts, or a queue too long to work, describes a false-positive problem instead: alert fatigue, which in time produces false negatives of its own because real alerts get dismissed with the noise.