When I first asked the question, above, about different ways that people conceived of synchronicity, I had handy a long journal entry on the topic. Rather than front load readers, I figured I would ask others first, as I wasn't satisfied with what I had come up with at that point.
The journal entry isn't handy, but I will see here what I can recall, to give an idea.
First, there is the salience threshold .... at what point do you say .... "okay, that's synchronistic!"....? If I go town A and see a black dog with a red bandana, and then later that day in town B see a black dog with a red bandana ... that is probably still below the threshold. If, however, in each case, as I was driving by, I see both dogs lurch free of their owners to chase an orange cat, that would probably be above the salience threshold. If both dog owners were frail, kindly old ladies with blue hair and wearing a black shawl... that would definitely be above the threshold. It is reasonable to say that it is "Z-like" ("Z" being the traditional variable used to describe deviation from the norm ... the greater the absolute value of Z, the less likely for an event to occur ... at Z>3, an event would occur by chance just one time in twenty, if I recall right. Incidentally, those of you that like to have fun with data and perceptual filters, it takes some doing, but you can learn to perceive the world at a level of "Z-scape" where in events going on in your experience stand out primarily as levels of liklihood or not.)
Then, there are the separations in time and or space: as above, the two events (the first, by the way, is the 'reference event', the second is the 'instantiation event', for lack of better terms) are fairly separated in both time and space. Some are separate only in time (same park, different dogs, different hours, say), and others only in space (same park, different dogs, same time).
Then there is the issue of personal relevance: if you see the same 4-digit number twice in a day, say, a phone number and a building number ... well that is beyond one in twenty, probably, but if you are not calling the number nor have any business at the address ... what might that be about? especially if you dial in the local radio station and it turns out to have the same frequency (number). At any rate, synchronistic events have a degree of personal relevance... a synchronistic pair involving, say, owls, would seem to be of more consequence to a person that really liked those kinds of birds, or was fascinated by them, in some way, than, say, a 4 digit number.
Relatedly, some seeming synchronicities are "pre-referenced" in that ... oh, say, someone says "47 is my lucky number" , or "whenever I see a hummingbiird, real or a picture or a figure, I will come across a lost pet of someone's". So that is another variable. Within this group are standing references, as those two mentioned are, or spot-reference events ... as in, and I used to do this often, pre-decide before walking the dog that if on doing so, I saw a cat first, would take one course of action, a dog first, another, and other animal, neither.
Some synchronicites are experienced by just one observer, others, by more than one.
Others appear to indicate a specific meaning: Here: I have lived in Helena for well over a decade. They don't salt the winter streets here because it creates a major problem with the health of streams and rivers here, something that has a high value to the residents. As a consequence, the winter streets are typically hazardously icy. Nasty as they are for pedestrians, I rarely see someone slip and fall. Yet a few years back, while walking to the library, perhaps a mile or so, I saw two women, hundreds of yards and ten minutes apart, slip and fall on their faces, with sufficient effect in both cases to borderline require a doctor's visit. They were both dramatic, both happened exactly when I was looking at them, I was perhaps 20 yards away in both cases. Both women were being escorted by men. Save TV sports, I don't recall ever having seen anyone in my life having fallen on their face. This appears to have been a specific indicator ... yet nothing else transpired. Niether I nor anyone that I knew suffered a 'loss of face'; there was nothing that I could tie this High-Z event to. I still have no clue what that was about. My best guess is that, contrary to new-agey ideology, really high Z random events and event pairs DO occur.
Some Synchronicities indicate a course of action, others don't.
Then the whole business seems somewhat related to omens ... Omens can be like synchronicity in that there is an indefinite salience threshold. These, more than synchronicities, can have an utterly unearthly flavor to them .... Once, on a beach in Bradenton, I looked up and there was a cumulus cloud, pretty much by itself. It looked exactly like some God, in incredible detail ... looking toward the South (which would have been Northern South America), and with great sadness. This had the perceptual impact nearly equal to what it would have had an actually god come floating through. There were hundreds of people on the beach, by the way, and no one else noticed it. I have absolutely no idea what that was about either, and no awareness of some horrible event (I did have the feeling of some sort of injustice going down) happening at that moment, especially that might have been comparable to so many others as has happened there in the 20th century. I looked at 'god' and wondered "What...? What...??!, but was never clued in. So, another reasonable axis to consider is ... how to label it...? Sense of realness, or unrealness, if you prefer. It is related to reality-intensity (in your travels, it is easy to note that some things (including especially beings) appear to be 'more real' or more intensely so, than others).
And then there is the whole business of synchronicity frequency .... this is the only place that I have noted anything like a pattern ... there are some periods in life where they are much more frequent than others. During those periods, I seem to have been much better integrated with some sort of 'mystical flow' where everything seems to go right, or at least, much much better than usual.
More to say, but the post is already a long one.