This is not a trick question, but I’ve noticed that the likelihood for one to say “yes” or “no” is largely dependent first on age, and second on what it was that got one interested in the scene in the first place.
First off: What Mod Is
“Mod” is a subculture originating in the UK in the late 1950s. Depending on who you ask (yes, even those “who were there”), the term may or may not be interchangeable with “Modernist”. It’s generally accepted by cultural historians that Mod came about initially as the UK’s take on the US’s “beat generation”, and by about 1962, the scene had become commercialised and from about 1962 to 1968, “Mod” was pretty much a youth fad used as an adjective to describe cloths and haircuts; for the most part, the main people who will argue against this are self-proclaimed “first genners” who didn’t get into it until Ready Steady Go! permeated the after-school airwaves, starting around 1962. While the primary driving forces behind the Mod subculture are music and fashion (the historical and present importance of one or the other will vary, depending on who you ask), Mod is also loosely associated with art, literature, and philosophical movements that certainly pre-date 1958, and I will say until the day that I die that the origins of the subculture even go beyond that, and extend into the “flappers and shieks” of the 1920s. As a living, breathing subculture, it’s had changes over the last sixty years, and variations are generally accepted within the scene, even if a bunch of snooty people on the Internet might lead one to think otherwise.
Now the next part: What Retrofuturism Is
Retrofuturism is an art and literary movement, first and foremost, though in the last ten to fifteen years, fashion and music inspired by said art and literature has sprung up and made itself known, which may lead to the assumption that various retrofuturist categories are separate subcultures, though most people involved in retrofuturism tend to stress the art and literature movements over the idea that it’s about fashion and/or music —even long-time retrofuturist artists who also work in clothing/fashion and music stress the media as art, not as fashion.
As of the time I write this, the most popular retrofuturist movement are Steampunk, Dieselpunk (and its offshoot Decopunk), and Atompunk. The terms came about as a tongue-in-cheek reference to the “cyberpunk” science fiction movement, which has little to do with the punk subculture, but cyberpunk certainly seems to regard its aesthetic and “attitude” as inspired by some of the more affectionate stereotypes of the punk subculture. The prefixes, as with cyberpunk, allude to the “technology ages” of the 19th and early-to-mi 20th Centuries that the classifications take their inspirations from. Steampunk is therefore a science fiction setting based on Victorian and early Edewardian “steam powered” technology. In the late 1910s, the rise of the diesel engines came about, so Dieselpunk has an aesthetic and makes use of technologies based on what was available from about 1915 to 1950. Atompunk is about the “atomic age”, about 1945 to 1970 (though it can extend to 1980), and is still arguably the most “futuristic”-looking of the main three (excluding cyberpunk, which tends to consciously reject “retrotech”).
Steampunk is the oldest of the styles, not just in aesthetic, but as a potential future aesthetic. The sub-genre of sci-fi has been retroactively applied to the writings of Jules Verne and others. Films like Metropolis and HG Wells’ Things To Come are regarded by Deiselpunk fans as prototypical masterpieces of the subgenre and aesthetic. While I’m at a loss to think of early examples of Atompunk, the Church of the Subgenious and the band DEVO certainly make copious use of atompunk imagery.
There are further subgenres. If the story or the aesthetic is based on clockwork technology, a handful of Steampunk purists will call it “clockpunk”. If the technology is based on the early age of electricity, especially the works of Nikola Tesla, a few handfuls will argue that it’s neither Stem- not Dieselpunk, but Teslapunk.
On Dieselpunks.org, and a few other places on the Internet, there is argued to be a bit of a divide between Dieselpunk and Decopunk (or Dieselpunk Deco, as I sometimes see it referred to) with the assertion that Dieselpunk is gritty, grimy, almost ultra-noir, and has higher tendencies toward dystopian settings (like the video game BioShock), whereas even when Decopunk has darker themes, it’s shinier and usually more optimostic in tone. Gatehouse Magazine also describes the divide as “Piecraftian” (gritty, dystopian) and “Ottensian” (shiny, optimistic), and Ottens himself has even gone so far as to suggest that Ottensian/Decopunk is the ideal Dieselpunk subgenre for returfuturism.
So now: Whether or Not Mod qualifies as Retrofuturism
Due to the origins of Mod laying ostensibly in late 1950s London, England, though a handful of people (including myself) placing its gestation over thirty years prior, it’s really easy to be tempted to associate Dieselpunk or Atompunk with Mod, and going by some of the more avant-garde fashions from the mid-to-late 1960s (often modelled by Peggy Moffitt), it’s certainly understandable that atompunk and early space-age science fiction would certainly appeal to the Mod scene, and on the forum on Dieselpunk.org, the love of crime noirs is apparent, and crime noir has been a staple of the Mod scene for decades.
That said, while it’s indisputable that there’s a subculture growing around the retrofuturist literary and art movements, this is something that, by and large, developed wholly independent of the Mod subculture, and Mod has likewise developed largely independent of retrofuturism (or what would later be dubbed such), even if certain retrofuturist aesthetics can certainly have high appeal to Mods. It’s as inaccurate to say that “Mod is retrofuturism” as it is to say “punk has nothing to do with rebellion”.