The standard intellectual approach to defining generations is to lump together those individuals who all went through some key event or series of events during the same stage of their life. The point is that what shaped the members of a generation, and what binds them together, is meaningful — growing up in Postwar prosperity, as children of divorce, as digital natives, etc.
In an informal setting, though, the shared traits are not so meaningful. What's your slang word for "very good" — is it "peachy keen," "groovy," "sweet," or "amazing"? (Those are for the Silents, Boomers, Gen X, and Millennials.) What were the popular colors for clothing when you were in high school? What are your favorite pop songs of all time? Who was your first huge celebrity crush?
These are not the kinds of people-molding forces that social scientists propose.
Sometimes the two approaches will draw similar boundaries — if you were a child of the Postwar prosperity, and born during a time of rising fertility rates, you are also familiar with the phrase "groovy," at some point in high school you wore orange and blue on the same day, one of your favorite pop songs is "Happy Together," and you had a huge crush on Mary Ann or Ginger.
But other Powerful Societal Forces don't affect people for a limited time to produce a tightly bound generation who underwent the effects. They are long-term trends along which people born in one year or another simply came of age during an earlier or later phase of the single ongoing process. Suburbanization, ethnic diversity, mass media saturation, and so on.
Gen X and Millennials, for example, don't look like distinct generations when you look at those three factors — they look fairly similar to each other, and different from the Greatest Gen, Silents, and even Boomers. And yet their group membership badges are totally different — slang, "you can't listen to that, that's our song", or tastes in food (way more toward Mexican and Chinese slop among Millennials).
When the X-ers and Millennials vote against the "boo taxes" government of the Silents and Boomers, it will be a case of politics making strange generational bedfellows, not similarly shaped generations on either side warring against their antitheses.
The choice of whether to carve out groups based on a meaningful or arbitrary trait shows up in evolutionary biology and historical linguistics. Both fields prefer shared traits to be arbitrary. If lots of individuals share something seemingly arbitrary, it's probably because they come from a common origin where that just happened to be the norm. That's why geneticists look at neutral DNA to determine ancestry.
If lots of people share something meaningful, like dark skin, that could be due to similar meaningful pressures acting on two unrelated groups, like the Africans and New Guineans both evolving dark skin as an adaptation to tropical climates, despite being distantly related on the whole genetically.
Likewise in the history of language, if two groups share a word for something functional like "internet," that could be because two unrelated groups both adopted the phrase when they adopted the technology, in recent times. If they share a word for the number "four," that can't be chalked up to similar pressures making the groups speak similarly. They must descend from some common ancestor where the word for that number just happened to be pronounced "four".
Aside from the theoretical motivation for using arbitrary traits, they're also the most palpable in real life. If you overhear someone in line at the store saying they agree with gay marriage, that is most likely to be an airhead Millennial, but could very well be an X-er or even a Boomer. Ditto if they make an offhand joke about their parents' divorce, their student loan burden, and the like.
But if you overhear your fellow supermarket shopper say, "Listen, they're playing "Footloose" — isn't this song suh-WEET?!" then they're definitely Gen X. If it's, "Oh my gosh, I'm like obsessed with "Blank Space" — not gonna lie, that song's actually kind of amazing!" then they're literally definitely Millennials.
The sociologist's large-scale impersonal forces make individuals similar, but not necessarily in a social dynamic way that cements group membership. Children of prosperity turn out this way, children of austerity turn out that way, whether they ever interacted with other members of their group to create a shared culture.
It's the seemingly trivial stuff that serves as shibboleths, food taboos, folk tales ("urban legends"), and totem animals to distinguish Us from Them. Those things only became popular by individuals accepting them rather than any of their alternatives to signal what group they belonged to. They get closer to what creates a community, beyond what creates a group-of-similar-individuals.