Vector commitment allows one to commit to an ordered sequence of $q$ value ($m_1,\cdots,m_q$) in such a way that one can later open the commitment at specific positions(e.g., prove that $m_i$ is the $i$-th committed message).
A Zero-knowledge set means that users commit to a set and subsequently prove the (non-)membership of some elements without revealing any further information (not even the cardinality of the committed set).
Accumulator allows to succinctly present a set by an accumulation value with respect to which short (non-)membership proofs about the set can be efficiently constructed and verified. Zero-knowledge accumulator additionally provides hiding guarantees: Accumulation values and proofs leak nothing about a set.
Zero-knowledge Elementary Database allows to commit a database that consists of the pairs $(i, DB[i])$ and prove that $DB[i]$ is the value on position $i$ without revealing any further information.
I confuse these primitives. The zero-knowledge set and Zero-knowledge accumulator set are designed for unordered data. Vector commitment and Zero-knowledge Elementary Database are designed for ordered data. Could these primitives be transferred mutually? What's the difference. Could we say that Vector commitment is Zero-knowledge Elementary Database?