How do different dendritic spines experience a correlated/coupled calcium signaling? The following quote from the discussion in a review paper by Higley and Sabatini:


  Finally, several studies demonstrate the ability of dendritic Ca
  transients to herald near-synchronous and spatially clustered synaptic
  activation. However, most of this evidence has been acquired in brain
  slices using forms of synaptic activation that may not closely
  resemble in vivo conditions. The intact brain is awash with robust and
  behaviorally context-specific patterns of synchronous neuronal
  activity (Buzsaki and Draguhn, 2004; Llina´ s and Steriade, 2006;
  Stevens and Zador, 1998).
  
  Moreover, neurons in vivo are influenced by both excitatory and
  inhibitory synaptic connections as well as state-dependent actions of
  myriad neuromodulators.


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

made me pondering about the following questions:


What's the difference between Calcium signal into the spine versus "Ca transients"? 
How do different neurons/spines have a coupled/correlated calcium signal?
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).