Disclaimer: potentially divisive subject matter! If this is a something that interests you and you're open to some healthy conversation, keep reading! If you've already seen one too many slope-shoulder dreadnought vs jumbo threads, get out while you can! If you're undecided, enter at your own risk!
Dreadnoughts and jumbos: some brief historical context
In 1934, Martin introduced the modern "dreadnought" with their 14-fret D-18 and D-28 designs. The same year, Gibson introduced their 14-fret "jumbo" model, which would eventually evolve into the J-45 and a handful of other guitars.
Aside from a detour Gibson took with the J-45 (and other models that shared the design) in the 60s/70s/80s, the Martin and Gibson shapes remain relatively the same today, with some very slight variation over the years due to manufacturing changes and such.
Here's the confusing part: decades later, many now refer to the J-45 and similarly-shaped guitars as a variation of "dreadnought" style guitar. Others insist on the original "jumbo" name. Who's wrong? Who's right? And why?
I thought it might be helpful to compare the two silhouettes, as well as some others for context.
Dreadnoughts and jumbos: a visual comparison
Another disclaimer: these shapes aren't exact facsimiles, but are tracings I've done to scale that should be close enough for our purposes. Apologies that the text and lines are a little grainy — it appears the images got overly compressed at some point.
Let's look at the D-28 and J-45 shapes.
There are subtle differences to be sure — the shoulders being the primary deviation — but overall, the visual footprint of these shapes is very similar! It's not difficult to see why the guitars eventually have come to be categorized together.
Now, let's look at these two silhouettes with the context of a couple other shapes from the same brands. Several years after introducing the "Jumbo" model, Gibson launched an even larger guitar with their "Super Jumbo" style, included here. Also included is the Martin 14-fret OM/000 shape, which was introduced four or five years prior to the 14-fret dreadnought shape.
The similarities between the D-28 and the J-45 become even more apparent when looking at these other two shapes from Gibson and Martin. The wide waist and the pear-shaped silhouette look nearly identical when compared to the narrower waists and different sizes of both the SJ-200 and the OM-28.
Now let's look at the D-28 and J-45 along with a few other similarly-sized guitars.
Like the first image, there is some slight deviation between the silhouettes, with the primary differences being at the shoulders — the Hummingbird being slightly more squared off, and the J-45 and 717 models a bit more rounded. Overall, however, they're all a lot more similar than they are different.
Finally, let's bring the SJ-200 and OM-28 back into the mix, along with another familiar "jumbo" shape from Guild and an "auditorium" shape from Taylor.
It's clear where the deviations are — the tighter waists of the auditorium sizes and the wider, more rounded lower bouts of the jumbo sizes are obvious outliers here, while the dreadnought sizes look even more consistent with the contrast of the other styles.
Dreadnoughts and jumbos — some final thoughts
So... are the J-45s and similar guitars dreadnoughts or jumbos? I believe the answer is a resounding... yes. Historically, there's no denying the Gibson style was called a jumbo. But it's also very clear that the style's silhouette shares more than a little in common with the Martin equivalent, and that most players, brands, and builders choose to categorize them together with the now-ubiquitous Martin term.
How did this happen? While these terms were initially more closely associated with specific brands and models, they have since become industry-wide sizing classifications, elevating them above use exclusive to a particular brand or model.
Part of the reason this happened was that the Martin and Gibson brands continued to make more guitar styles, and weren't always consistent in how they classified their guitars outside the model name.
For instance, the D-18 and D-18 were initially called orchestra models along with the other models with 14-frets clear of the body. The 14-fret dreadnought was even referred to as a bass guitar early on. Gibson introduced larger guitars after their original "jumbo" guitars with the larger SJ shape, and later the square-shouldered Hummingbird shape. By 1960 they were classifying all of these guitars as jumbos.
Another huge factor has been the ever-expanding number of guitar brands and builders over the years since Martin and Gibson introduced these shapes. Many of these newer guitars have been inspired by and patterned after these two classic and successful Martin and Gibson shapes. As such, there was a need for an industry-wide term for guitars that shared the same overall silhouette.
Because Martin had been more consistent with their classification and had arguably been more successful and well-known, and because the jumbo term had come to be more closely associated with larger guitars, the dreadnought term was categorically used for guitars with the same overall silhouette as the Martin and Gibson shapes, with the latter shape often subcategorized as a slope-shoulder or round-shoulder dreadnought.
So in summary, someone who calls the J-45 a jumbo is right — it is, after all, what the 'J' stands for and was the original name for that Gibson body style. And someone who calls it a slope-shoulder dreadnought is equally right — today the guitar typically falls into an industry-wide, "dreadnought" classification, as supported by the visuals above.
Hopefully this helps clear up any confusion some might have about the these terms — apologies in advance for any errors. Thanks for humoring me and high five for reading to the end.