In the UK, if you're in a regulated sector e.g. financial services or health services, there are obligations relating to complaints handling. E.g. the Financial Conduct Authority sets out complaints handling rules in DISP 1.3.
The FCA says a complaint is:
any oral or written expression of dissatisfaction, whether justified
or not, from, or on behalf of, a person about the provision of, or
failure to provide, a financial service, claims management service or
a redress determination, which: (a) alleges that the complainant has
suffered (or may suffer) financial loss, material distress or material
inconvenience; and (b) relates to an activity of that respondent, or
of any other respondent with whom that respondent has some connection
in marketing or providing financial services or products or claims
management services, which comes under the jurisdiction of the
Financial Ombudsman Service.
So if there is "feedback" expressing "dissatisfaction" etc it is a complaint.
Some entities have acted such that they seem to believe a complaint must be submitted through 'proper channels' to be a complaint. E.g. a complaints form online, a complaints@companydomain email address or a letter addressed to the Complaints Department. Is that the distinction you are making?
But that is not the case in regulated organisations, where a complaint is "any oral or written expression of dissatisfaction..."
Now, in such an organisation you're not obliged to have a particular type of form or email address etc. But you are obliged to make the complaints procedure relatively easy and reasonably priced if not free (i.e. premium rate phone number for the complaints line = bad, local rate or freephone number = OK).