Distinguishing between plot types and story structures is often an incredibly subjective exercise, both because the analyst’s personal opinions can sway the designations and because stories are individual and eccentric creatures that don’t always fall into neat categories. That being said, as a writer trying to find a story, as well as trying to figure out what kinds of stories she likes and which kind to use, trying to classify story types can be helpful.
But I just want to warn you that this is a subjective and imprecise exercise that is certainly not based on absolute facts; and that my personal preferences are going to show, but that is no indication of either type having a superior quality.
There are many, many different types of stories, but one more general designation I like to think about is whether the plot is “immersive” or “daily life.” These categories can be applied to various plots like a setting or style, so they can work with many different types of stories.
Immersive plots are events which take over the protagonist’s life and become their entire experience for the duration of the story. These types of plots take the protagonist away from their daily life almost entirely, and nearly every beat of the story is a part of the plot. Generic examples include plots where the protagonist is kidnapped, where they must go on a journey, where they must stop a villain within a given time frame, where the world is being destroyed, etc.
Specific examples of immersive plots include: Lord of the Rings, where Frodo leaves his daily life in the Shire to take a journey to destroy the Ring; The Bone Season, where Paige’s captivity in Sheol makes the entire story about her attempts to survive and escape; The Hunger Games, where Katniss is thrown into the Games and the entire story is about her experience there; and any James Bond film where the story is about him being summoned from his daily life to complete a mission.
Daily Life plots are events which take place within the protagonist’s daily life, which continues as a part of the story throughout. In these stories, much of the “plot” takes place in the spare time of the rest of the character’s daily life, which may add subplots of its own. Therefore, some beats of the story may be elements of the character’s daily life that have nothing to do with the central plot, sometimes so many that the central plot may be hard to pinpoint. Generic examples include plots where the protagonist’s job brings them the plot (but keeps them busy with other things as well), where they are investigating on their own time, when they are experiencing romance in their daily life, etc. Sitcoms and soap operas are almost always daily life plots; most character-driven dramas are (except for road trip-type stories, or other unusual experiences that take up the entire story).
Specific examples of daily life plots include: the Harry Potter series (except Deathly Hallows, which is more immersive because of their journey), where Harry must continue with his schoolwork while dealing with various threats; Twilight, where the characters continue to go to high school; the Mercy Thompson series, where the plots interrupt Mercy’s daily life but not too completely or consistently; and series like Charmed or Buffy the Vampire Slayer, where the characters fight demons and vampires while trying to cling to a normal life.
And then there are the plots that aren’t so easy to figure out, since they combine elements of both. In The Rook, an excellent book I just read, the main character must try to live a life she has no memory of while trying to figure out who stole her memories and is still trying to kill her. Thus, there are elements of her daily life (her job, the people she can’t remember), but it’s within the “immersive” experience of trying to find her attempted killer and the dangers of “pretending” to be this person (it makes more sense if you read a full summary).
In a different vein, the movie Pacific Rim follows jaeger pilots fighting off kaiju, which to them is a relatively normal and “daily life” experience—however, in this particular plot, the escalation of the conflict and the desperation of the last few jaegers means that it’s more of an “immersive” story. The entire story is about this one conflict, so it falls more in line with immersive stories. This is often the case with stories where the character’s daily life and job may be dealing with ‘plots,’ but the specific story we see is one specific conflict and thus more immersive.
And, for a final example, Divergent follows a teenager undergoing what, in her society, is a normal daily life experience—choosing a faction and going through initiation. However, because of the specific threat to her for being divergent, she is under threat throughout the story. The pacing allows for more of a “daily life” feel, so I would argue it leans towards that, but the main conflict’s presence throughout might make it immersive. This is an example of how subjective this distinction can be.
Neither type of plot is inherently better than the other, as you can see successful examples in each (and see where they blend and make the separation entirely moot). Immersive plots tend to be more suspenseful and fast-paced, since the conflict is omnipresent and constant. Daily life plots generally follow a slightly slower pace, since they are allowed to linger within the character’s life outside of the plot (though those scenes/sequences still have to have their own conflicts). Most episodic conflicts, such as TV shows, are daily life plots; the exception is ongoing plots of which each episode is just a chunk, like Game of Thrones or Scandal (when it’s not episodic).
My personal preference is for daily life plots, since they often focus a little more on character and their relationships. However, these types of plots are only interesting if the daily life is fascinating and/or fun (such as being at Hogwarts), or if the tension between the daily life and the plot is compelling (such as in the case of stories where the protagonists want a daily life but it keeps being interrupted or must be kept secret).
I don’t know if choosing a type before you start defining your story is helpful. My personal brand of creativity doesn’t really pop entire stories into my head, so I sort of have to build them, and choosing generic plot types gives me parameters to work with. But if you have your story in mind already, it probably has a type inherent in its structure—and again, neither one is better than the other.
And you can always have a bit of both.