There is a difference between, correction, corrective action, & preventive action when a non-conformance is raised.
Correction can be applied at the time of the finding. Similar to your instance of a dirty piece of equipment. You found it, had someone re-clean and release for usage. This should be documented in your pre-op inspection. Things happen.
Corrective action takes it to the next level. If you see this equipment dirty each time you inspect it then there is a trend and this should be addressed with a root cause analysis. Why is this always dirty? Formally correcting and addressing the issue.
Preventive action is stating how do we prevent reoccurrence once and for all. Training, further evaluating the SOP, etc. More of a systematic approach.
Corrective action and preventive action can be one straight through process, we found an issue, we corrected it, reviewed root cause, then found a way to prevent in the future.
All are documented, but a formal CAPA is more detailed as this is stating things have escalated to an unwarranted or unsafe level.