In the study of temporal graphs, only paths respecting the flow of time are relevant. In this context, many concepts of walk disjointness have been proposed over the years and the validity of Menger's Theorem, as well as the complexity of related problems, have been investigated. Menger's Theorem states that the maximum number of vertex/edge disjoint paths between two vertices equals the minimum number of vertices/edges required to disconnect them. This paper introduces and investigates a type of disjointness that is only time-dependent. Two walks are said to be snapshot disjoint if they do not use edges active in the same snapshot. The related paths and cut problems are then defined and proved to be W[1]-hard and XP-time solvable when parameterized by the solution size. Additionally, in the light of the definition of Mengerian graphs given by Kempe, Kleinberg, and Kumar in their seminal paper (STOC'2000), we define a snapshot Mengerian graph as a graph G for which there is no time labeling for its edges where Menger's Theorem does not hold in the context of snapshot disjointness. We then characterize Mengerian graphs in terms of forbidden structures and provide a polynomial-time recognition algorithm. All our proofs work on the strict and the non-strict cases. Finally, we also present results about problems defined by similar types of disjointness, namely, multiedge disjointness and departure time disjointness.