How can different ion channels of the same type have different cell responses?
Quibbling about other types of LTP (not mediated by NDMA receptors) aside, this is a good question, with a rather intricate answer.
Basically (NDMAR mediated) LTP is not merely activated by calcium, but rather by CaMKII, which essentially acts a sort longer-term chemical memory for calcium that was once &quot;detected&quot; in a spine. A couple of points quoted from a fairly recent review paper:


[a] bulk calcium signal, when produced by depolarization of voltage-dependent calcium channels, is not sufficient to activate CaMKII.

a calcium signal will stay largely within the activated spine. The next step in the long-term potentiation cascade is the binding of calcium to the four binding sites on calmodulin. Calcium-saturated calmodulin keeps calcium bound for ~1 ms, a long enough time for calmodulin to diffuse within the spine and to bind CaMKII, but too short a period of time to diffuse out of the spine. [...] CaMKII diffuses at a very slow rate (for CaMKII to exit spines may take many minutes), activated CaMKII is mostly localized to the activated spine.



So basically a fast signal (calcium) gets converted into a (spatially) slow but locally persistent CaMKII signal (via calmodulin). As I understand it, anyway.