The relationship is that both are dimensions.
Dimensions is a very misused word. A dimension is a mathematical model that calibrates, measures and indexes an aspect of reality using standard units. Dimensions are abstract overlays that quantity underlying reality for us.
So, in the context of Space and Time, Space is the dimension of position and relative position. The xyx-axis allows us to define a position (in space), and relative positions distance. But its a static dimension until we introduce Time, the dimension of change.
So space, measured in say miles, gives us the quantification of the change of relative position. And Time, in say units of hours, gives us the rate of change (hence time is the dimension of change).
Ergo MPH – Miles (space) Per Hour (time)
So merge the dimension of [relative] position (Space) with the dimension of change (Time) and you get Spacetime, the dimension of changing position…aka motion.
So Time and Space are not interdependent. But Space is static without Time.