SQC 1 says that audit firm is suppose to maintain systems at firm level to achieve quality in audit with above things as ultimate objective. Such principles will be applicable to all assurance & related assignments of the firm as per SQC1.
On the other hand SA 220 deals with implementation of firm level quality control system to individual engagement level. Is applicable only to audit of historical information. It casts responsibility on engagement partner to implement quality control procedures.
SQC 1–> Firm Level Quality Controls + For all the types of assignments (Audit / Review / Assurance / Related Services)
SA 220–> Implementation of firm level controls to individual assignment level + only for audit of historical information
Because SA 220 is implementation of firm level controls as given in SQC 1, majority of concepts are same.