Well, I can really only speak to a few of the anime shows. The main theme is usually:
Bad Digimon are doing bad things. A rag tag group of kids, along with their Digimon partners, must put an end to the shenanigans with the power of friendship.
There is continuity between Digimon Adventure 01 and 02. There have been a plethora of movies around this particular group of kids. It's great.
The third series does a reset and everything is mostly stand alone from there. Some play a bit more fast and loose with things like digivolution tracks and whatnot, but the main themes are still there. Mostly they just want to bring peace to both the "real" and Digital worlds.
So in Pokémon, The animals are all naturally occurring monsters that live in the world, but wasn't Digimon like a digital animal where you had to raise it? are Digimon also naturally occurring creatures that live in the Digimon worlds, or are they virtual like computer programs?
The original Digimon Tamagotchi toys weren't super cannon to the lore that got built up in the animes. They were more akin to the Pocket Pikachu in that you were just raising a lil guy.
In the shows, the digital world is a consequence of technology. Kinda. It's accessible via computers and stuff. It is, like, "housed" on the internet, but it's a fully parallel universes (basically). This can change a bit per series (or maybe I'm misremembering).
Digimon live there naturally and have their own wants and dreams. Some are more animalistic in nature and intelligence, but most are sapient and can speak. Some Digimon are a direct result of humanity's thoughts and feelings and are based on real world myths. Others seem to be wholly unique creatures.
In "the wild" Digimon can Digivolve naturally based on their age. This type of Digivolution is seemingly permanent. If the Digimon is paired with a human partner, and there is a Digivice involved, they can attain higher levels without needing to age up, and they can return to their previous state after a time.
The Digivolution track is not linear. What branch they go down depends on a few factors, but is mainly an emotional thing. An angry Digimon will Digivolve into a different form than the same type of Digimon that is happy. In Digimon Adventure 01 for example, Greymon will normally Digivolve into MetalGreymon. One episode he is forced to Digivolve by his partner though, and becomes a much more evil SkullGreymon. When Digimon Digivolve they mostly maintain their memories, but the new forms can sometimes come with drastic personality changes. Kinda like how Ash's Charizard was obstinate compared to the much more agreeable Charmander it started out as.
In the digimon adventure 1 and 2 storyline, digimon are digital lifeforms created by a team of researchers and grew on their own from there.
Outside of that, at least as far as I've seen, kids get partnered up with a single digimon who through their bond can make their partner digivolve into different forms with distict levels, but their normal state is generally the rookie level, so after a fight they'll de-digivolve back to rookie regardless of what level they went up to.
oh, that's interesting. so a key difference between this in Pokémon is that instead of a team they just have one Digimon who's like their best virtual pet pal.
huh cool.
very interesting about the researchers creating the Digimon also, thanks. That's the stuff I'm looking for!
Just to clarify a bit: Digimon are not pets. They're always treated as friends. Well, in Digimon Ghost Game the main Digimon Gammamon (best boi) is more treated as a little brother. He is very young though, and has the mind and mannerisms of a young child. When he Digivolves he gets more mature, but after fights he's back to young little Gammamon.