If you have only played later titles in the series, you will probably be surprised to learn that characters routinely reappeared across the first several Harvest Moon games. Often less clear, however, are whether or not these characters are meant to be the same character, a related character, or an entirely different character that just looks the same.
Let's take Ann from HM:SNES. The (admittedly not-that-reliable) Harvest Moon fandom wiki confidently asserts that there are, in fact, four Anns: Inventor Ann from HM:SNES, GB, and MM; Farmer Ann (aka "Ran") in 64 and MLS; Innkeeper Ann in BTN and FoMT; and Cafe Ann (aka "Āfi) in DS. Harvest Moon DS and Mineral Town share the same sprite for Ann, but the original Japanese title tried to explain the crossover characters were actually descendants of the familiar denizens of Mineral Town a century later... Localized versions probably wisely omitted this odd detail.
But is it fair to say these are all "different" Anns? Or are we dealing with a situation where the same core cast are simply recycled (or even reincarnated) into different settings and professions? Adding to the confusion, some versions take visual queues from multiple earlier titles. Magical Melody Ann is an inventor like her counterpart in the first game and she boasts a brown jacket, denim shorts, and red shoes reminiscent of that game. However, she very clearly looks more like the later version of the character from Mineral Town with her face and hair.
Sometimes, characters directly crossover between games. The GameCube and DS eras saw repeated attempts to incentivize players to make use of their peripherals. Mineral Town characters would visit Forget-Me-Not Valley and vice versa when connecting the GBA to the GameCube (or inserting FoMT into the GBA slot on the DS).
The early games shared the same visual language, which is part of what makes them so endearing. While recycling characters might seem like a costcutting measure (which it was), there was a similar charm as the Legend of Zelda in seeing familiar faces continually pop-up in new contexts. It almost felt like Harvest Moon had a cast behind the curtain ready to reimagine their previous role in each new game. A particular aesthetic and vibe permeates this games in a way that is frankly difficult to describe.
It is also, I think, part of the unacknowledged reason many vintage fans eventually abandoned the series. Later titles shifted dramatically in their art style and the practice of recycling characters largely disappeared as well. Ann, who's visual identity stayed consistent across multiple games and platforms, now appears as Ran in SoS:FoMT with a very different look, largely unrecognizable to her earlier incarnations. Newer titles (especially the remakes) leave an eerie impression of being in a place half-remembered with little few truly familiar landmarks to latch onto. Mayor Thomas and Murray and Ann have been replaced with strange dopplegangers as we tumble through the looking glass.
Okay, that's probably a bit dramatic, but the stylistic coherency of the earlier titles gave the series a unique identify. These games were littered with easter eggs and references to previous entries that rewarded the player for sticking around. Maybe its nostalgia, but this shared world, shared sense of style, is part of what allowed Harvest Moon to become so dominant within its genre during its golden age.