Suppose that I, a college student, found a student organization—a chapter of Students Against a Democratic Society, perhaps. At the first meeting of SADS, we get to talking, and discover, to everyone’s delight, that all ten of us are fans of Star Trek.
This is a shared interest.
A shared interest—in the way I am using the term—is nothing more than what it sounds like: an interest (in the broad sense of the word) that happens, for whatever reason, to be shared among all members of a group.
The distinction I want to draw is between a shared interest (of a group) and a collective interest (of a group). The former is a superset of the latter; all collective interests are, by definition, shared interests; but not all shared interests are collective interests.
What is a collective interest?
Well, suppose that I found another student organization (extracurricular activities look great on a résumé). This one is a Star Trek fan club. At the first meeting of Campus Trekkies United, we discover, to no one’s surprise, that all fifteen of us are fans of Star Trek.
… well, of course we’re all fans of Star Trek. That’s why we’re in the fan club in the first place! Anyone who’s not a fan, has no reason to join the fan club. And so: Star Trek fandom is a collective interest of Campus Trekkies United.
A collective interest is an interest that is shared by every member of a group in virtue of being a member of that group. Anyone who does not share that interest, will not be a group member. And thus, by modus tollens: anyone who is a member of the group, will share that interest. It is guaranteed that every member of the group will share that interest.
Details & implications
Several important consequences follow from this.
Preservation of interests
Unlike a collective interest, a shared interest is not at all guaranteed to stay shared among all group members. Nothing stops someone from joining the Students Against a Democratic Society, who does not like Star Trek. At that point, Star Trek fandom ceases to be a shared interest of SADS. (Which may lead to some awkward consequences if, for instance, we had decided to start wearing colorful jumpsuits to our political rallies.)
I said earlier that “[i]t is guaranteed that every member of the group will share [a collective] interest”. But is this really true? Well, it’s true if the condition for an interest being a collective one holds: that anyone who does not share the interest, will not join the group.
But it is dangerous to simply assume that this condition holds, in the absence of any mechanism by which it is ensured to hold! Is Campus Trekkies United actually making sure that non-Trekkies do not join? Certainly it seems like they have no reason to want to join, but is that sufficient to keep them out?
Suppose a fan of Star Wars, incensed at the idea that the university would grant meeting space and funds to fans of the rival franchise, decides to pose as a Trekkie, and signs up for Campus Trekkies United under false pretenses. He hates Star Trek, and wants nothing more than to see the club cease all Trek-related activities, and transform into, say, Campus Jedis United. Now Star Trek fandom is no longer a collective interest of the members of Campus Trekkies United—because they did not ensure that the condition of a collective interest holds.
In fact, it would be more precise to say that Star Trek fandom was never a collective interest, only ever a shared one—because the condition of a collective interest never held in the first place!
The universal collective interest
A collective interest of Students Against a Democratic Society (ostensibly) is being against a democratic society. A collective interest of Campus Trekkies United (ostensibly) is being a fan of Star Trek.
But there is one sort of collective interest that will be present in any organization:
The continued existence of the organization itself.
Groups are how humans achieve their goals. Organization is power. It is in the interest of any member of an organization that the organization continue to exist. Any other shared interest may fail to be a collective one—except for this one.
Suppose that a proper subset of a group’s members share a certain interest. This may be coincidence—nothing more than a consequence of base rates of that interest in the general population. But it may also be due to the fact that a proper subset of the group’s members itself constitutes a coherent group, which has collective interests of its own.
This also manifests in a more interesting way, as follows:
Suppose it is claimed that a certain interest is a collective interest of a given group. However, investigation reveals group members that do not share that interest.
The claimant(s) may cry “No true Scotsman”, “infiltrator”, etc. But another (and, it seems to me, more likely) explanation is that the claimed collective interest is indeed a collective interest—not of the whole group it’s claimed of, but rather of a proper subset of the greater group (which subset, however, may find it advantageous to be identified with the greater group).
(Finding examples of this dynamic is left as a fairly straightforward exercise to the reader.)
 Note that the inverse—that anyone who does share the interest, will be a group member—need not be true!