The display critically has a messed up timeline.
First up, we've Fate/Zero which takes region 10 years previous to the ‘major story’.
Zero chronicles the Fourth Holy Grail War and focuses specially on Emiya Kiritsugu.
Okay so subsequent, we've Fate/Stay Night (2006), Fate/Stay Night: Unlimited Blade Works and sooner or later Fate/Stay Night Heaven's Feel. (Note: The Heaven's Feel collection is a three-part movie series and only one movie has been released.) All three collection focus on Emiya Shirou, Kiritsugu's adopted son and his involvement inside the Fifth Holy Grail War.
So you need to keep in mind that those 3 anime take place across three parallel timelines. The predominant difference being the affection interest and common cognizance. The 2006 version, aka the Fate Route, has Saber as Shirou's love hobby and focuses particularly on her courting with Shirou and her form of twisted beliefs.
( Image : google )
Unlimited Blade Works has Rin Tohsaka as the love interest and focuses closely on Shirou's very own ideals as well as Archer's real identity.
Finally we have Heaven's Feel which has Sakura as the love interest and focuses quite closely at the proper nature of the Grail itself.
And of path, we've got Fate/Apocrypha, Fate/Extra, Fate/Grand Order and Fate/Kalied Liner Prisma Illya which can be all spin-offs. And then in the end Carnival Phantasm and Today's Menu for the Emiya Family which might be parodies.