Here's the ISO definition of correction:
I'm not sure where people are coming up with the idea that correction includes containment. If anything, I would say that containment of a nonconformity is more likely include correction. Unfortunately containment is not defined in any ISO document that I'm aware of.
Generally all of these terms are used in the context of corrective action for a nonconformity. Correction eliminates the nonconformity, while corrective action eliminates the cause of the nonconformity and prevents recurrence. Containment is something that we do to keep the effects of the nonconformity that already exists from causing further problems internally and with our customers.
Any way you look at it, containment is a good idea and should be considered along with each nonconformity encountered.
I have seen containment as part of the correction portion of nonconformances from CB auditors using the CB's form.
ANAB Heads Up 137 provides a bit more detail and may help to see where it came from. This ANAB publication is directed to CBs and how they answer nonconformances written against them by ANAB, but the principles are much the same, and it was passed on to auditors as an example by many CBs. Here is the pertinent portion:
Correction – in order to be fully accepted, the response must include the following components:
1. The extent of the nonconformity has been determined and contained
a. The nonconformity has been corrected and the response is written in the past tense. (E.g.
the missing record was found (not will be found)).
b. The CB has examined the system to see if there are other examples that need corrected
(extent of the issue) and have also addressed the extent in their response.
c. Including the evidence ANAB found and any other evidence the CB may have found.