Exploit
An exploit is a method, input, or piece of code that takes advantage of a vulnerability to produce an unintended security outcome.
The vulnerability is the weakness. The exploit uses it. A specially formed request or document might trigger behavior the application was not supposed to permit; an exploit does not have to look like a separate program.
MITRE documents exploitation against both client applications and internet-facing services. The required conditions vary. Some attacks depend on a person opening content, while others target a reachable service. Do not assume that every exploit needs a click or that every successful exploit grants administrator access.
Execution does not always mean exploitation
Someone persuaded to run an ordinary command may give an attacker code execution without any software vulnerability being exploited. The ClickFix article explains that social-engineering route. Calling it a software exploit would obscure the control that actually failed.
Likewise, public exploit code does not establish that a particular system is vulnerable or compromised. Its version, configuration, access requirements, and protections matter. An attempted exploit and a confirmed outcome should be reported separately.
When documenting an exploit, name the weakness it uses and the result you observed. Code execution, a crash, and access to protected data are different outcomes.