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Cambridge Dictionary gives this definition about "complain"
to say that something is wrong or not satisfactory
and this definition about "complaint"
a statement that something is wrong or not satisfactory
I guess both of them means the same thing. However, Google Ngram shows that the former is much more commonly used that the latter
Are those two expressions interchangeable?
Complaining about something is more likely to refer to making an angry or discontented comment about something in conversation.
"What dreadful weather we're having."
"The buses on this route are never on time."
Making a complaint is usually something more formal, such as writing a letter to the bus company.
To complain (simply that) can mean merely to say that something is unsatisfactory, e.g. John complained that his coffee was cold. To make a complaint is to start a formal procedure, either verbally or in writing, for example if you were rudely treated by a shop worker you might write a letter of complaint to the company, or seek out the manager and make a complaint verbally.
