No, normally, a procedure manual is not the same thing as a quality manual.
A procedure manual, normally, is considered as a compilation of all procedures of an organization. A quality manual, normally, is a document where the quality system of an organization is described together with its quality policy. Both manuals are not mandatory according to ISO 9001:2015.
Let me remark that I think that in older versions of ISO 8402, the vocabulary standard that became obsolete in 2000, there was a note saying that the sum of all procedures could be the quality manual. However, I never saw that approach followed in practice.