How do different dendritic spines experience a correlated/coupled calcium signaling?
With little to go on, your questions are difficult to answer specifically but I'll give the general guidance I can.

1) Calcium signals in neurons are typically brief. "Calcium transient" is a synonym for "brief calcium signal." Someone could contrast between types of calcium transients in terms of their source (external calcium vs. internal stores), location (spines vs dendrites), etc, but you would have to give a more specific example to describe any difference.

2) Calcium signals could be correlated in different neurons or different spines of the same neurons if both cells/spines get excitatory input from the same presynaptic cell, or if excitatory input is from different cells that have temporally correlated firing. You could also get coupling if the entire dendrite is depolarized, either locally or via a back-propagating action potential. Again, without a specific example it's difficult to give more information.

The review you cite:

Higley, M. J., &amp; Sabatini, B. L. (2008). Calcium signaling in dendrites and spines: practical and functional considerations. Neuron, 59(6), 902-913.

discusses both (1) and (2).