It's a bit more complicated than that. Given any two events, there is a quantity, called the interval (also 'spacetime interval' or 'invariant interval'), denoted $\Delta s^2$, and which equals $\Delta s^2=c^2\Delta t^2-\Delta \mathbf r^2$, which determines how the two events can relate to each other causally.
If $\Delta s^2>0$, then we say $A$ and $B$ are "timelike separated" (or lightlike separated if $\Delta s^2=0$). In this case all observers will agree that (say) $A$ happened before $B$, and $A$ can causally influence $B$.
If $\Delta s^2<0$, then we say $A$ and $B$ are "spacelike separated". In this case $A$ and $B$ are causally disconnected, and neither can influence the other. Different observers will disagree on their temporal order, and in fact you can always find observers for whom $A$ happened before $B$, $A$ happened after $B$, and $A$ happened at the same time as $B$.
Finally, is $\Delta s^2=0$, then we say that $A$ and $B$ are "lightlike separated", or that the interval between them is "null". This is identical to timelike separations: all observers will agree that (say) $A$ happened before $B$, and $A$ can causally influence $B$; moreover, a light ray emitted at $A$ in the direction of $B$ will reach that position at the exact instant that $B$ is happening, and it will do so in all frames of reference.
The set of all events $B$ which are at lightlike separations from $A$ is called the light cone of $A$, and it separates space in three regions: the interior, with timelike separations, itself split into the causal future and the causal past of $A$, and the exterior, with spacelike separations, which contains all events that are causally disconnected from $A$, and which are simultaneous with it in some frame of reference.
Thus, as you succinctly put it,
if $A$ and $B$ are linked (one causes the other), then they have to be timelike [or lightlike] separated and all observers will agree on their temporal order.