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While the PKI System deal with digital certificates life cycle and Key Management System (KMS) deal with keys life cycle.
KMS can manage certificates.
You are getting hung up on the "life cycle" terms and not looking at the big picture.
PKI is a concept. It is the infrastructure for the idea of public/private keys along with the processes and protocols to make it work. It introduces the idea of a CA along with defining their responsibilities.
KMS is a product. It answers the question, "what do I do with all these private keys I have from the CA?"
PKI has protocols and guidelines for dealing with certificate life cycles, but a KMS actually implements life cycle management for specific keys for a specific organization using PKI standards.
From the Wiki for KMS and PKI:
Key management concerns keys at the user level, either between users or systems. This is in contrast to key scheduling; key scheduling typically refers to the internal handling of key material within the operation of a cipher.
A public key infrastructure is a type of key management system that uses hierarchical digital certificates to provide authentication, and public keys to provide encryption. PKIs are used in World Wide Web traffic, commonly in the form of SSL and TLS.
