The RPG that you saw was an April fools Joke. (Correct me if I'm wrong.
No, Defiant of Shrine Maiden does exist - its expansion/sequal, Counterattack of God Human Being, is more popular.
is there some from of a story that continues through all of them, like I think there is with final fantasy, but I'm not sure as I haven't actually played final fantasy hehe.
Actually, the Final Fantasy games are totally separate worlds and stories each time.
Anyway, to best explain, Touhou is, as said, a series of games made by ZUN, which has expanded and flat out exploded in popularity, to the degree of which extremely few Doujin (Self-produced) products ever has (It could be likened to Fate/Stay Night's extreme popularity - but perhaps even bigger as far as fan creations).
The main series is focused on "bullet hell" gameplay, in which you need to carefully weave through complex and artistic bullet patterns, made possible only via the very small hitboxes. Touhou is set apart from other shmup series by the fair (and changeable) difficulty, focus on large numbers of fairly slow bullets to reward calm play as careful movement (as opposed to fast bullets and twitch dodging), rewarding the player for 'grazing' bullets (Almost, but not quite, getting hit) and playing riskily, as well as a sense of beauty and originality in the attack designs of bosses.
The other thing that sets it apart is story and character. A lot of bullet hell games ignore these things - Touhou games feature a pretty huge female cast (Each boss tends to be a brand new character) and a flowing story for each game (Although they're fairly independant, so you don't need to play each game).
The main two characters are Reimu Hakurei, a lazy human shrine maiden who fights off Youkai and goes to solve any and all major 'incidents' that occur throughout Gensokyo (The fantasy setting of Touhou), and Marisa Kirisame, a kleptomaniacal human witch and Reimu's friend; as well as other various characters throughout the series.
Technically, Touhou 1-5 are non-essential and just a sort of background image to Gensokyo at this point (Even the creator acts like it), so the Windows games, in order, are...
Touhou 6: Embodiment of Scarlet Devil - a strange scarlet mist covers Gensokyo, blocking out the sun, so Reimu and Marisa head to the mysterious Scarlet Devil Mansion to find out who's behind it. Lots of characters introduced here come back in later games.
Touhou 7: Perfect Cherry Blossom - Winter's over, but spring hasn't arrived! Reimu, Marisa, and the maid of the Scarlet Devil Mansion, Sakuya, head out to get it back. More refined than 6 and considered one of the best, and again, a lot of this cast comes back later.
Touhou 7.5: Immaterial and Missing Power - A festival for the girls turns into an all out brawl! It was only half-developped by ZUN; Tasogare Frontier mostly made this very unique fighting game.
Touhou 8: Imperishable Night - Realising the moon in the night sky isn't the real one, one of four teams of girls sets out to find the real full moon by extending the night. The Touhou game with the most content due to branching stages and unlockables, but also sorta gimmicky and easier than others.
Touhou 9: Phantasmagoria of Flower View - Flowers are blooming like crazy all over Gensokyo, and everyone's out and about to find out why! The game is a 'versus bullet hell', where you and your opponent are both trying to survive and overwhelm one another.
Touhou 10: Mountain of Faith - A whole mountain has appaeared in Gensokyo, so Reimu and Marisa go to investigate. Very much reverted to a simple game from the increased complexity of 8, opinions are mixed but the game's still solid.
Touhou 10.5: Scarlet Weather Rhapsody - Strange weather and earthquakes are hitting Gensokyo! Who's behind it? Well, you'll find out. Another Tasogare Fronteir fighter, which is getting an expansion soon. Easier to pick up and play than IaMP, but a bit more random.
Touhou 11: Subterranean Animism - A geyser opens near Hakurei shrine, so Reimu and Marisa head underground to stem a flow of evil spirits, accompanied by old friends. My personal favourite, but also known for being hands down the hardest of the bullet hell games.
There's also 9.5 (Shoot the Bullet, focused around photographing bullets, but has no active plot and stars Aya, from 9), and the upcoming 12: Undefined Fantastic Object (About a mysterious flying Treasure ship), and a TONNE of fangames - including platformers like Super Marisa World or MegaMari, RTS like Patch-con! Defend the Library, beat-em-ups like Rift in Friendship and Mystic Chain, other bullet hells like Concealed the Conclusion, and even RPGs like Touhou Mother.
The good news? A lot are
translated - 6, 7, 7.5, 8, 9, 9.5, 10, and 11 from the main series can all be patched to english, and so can a few fangames.
