In this paper we discuss relationships between client-centric consistency models (known as session guarantees), and data-centric consistency models. The first group includes: read-your-writes guarantee, monotonic-writes guarantee, monotonic-reads guarantee and writes-follow-reads guarantee. The other group includes: atomic consistency, sequential consistency, causal consistency, processor consistency, PRAM consistency, weak consistency, release consistency, scope consistency and entry consistency. We use a consistent notation to present formal definitions of both kinds of consistency models in the context of replicated shared objects. Next, we prove a relationship between causal consistency model and client-centric consistency models. Apparently, causal consistency is similar to writes-follow-reads guarantee. We show that in fact causal consistency requires all common seesionguarantees, i.e. read-your-writes, monotonic-writes, monotonic-reads and writes-follow-reads to be preserved.