What exactly is fate? Or type moon or whatever? Is it all the same but different like shin megami tensei stuff?

TYPE-MOON: an entertainment company that got its start as a creative duo that self-published its works, originally consisting of writer Nasu and artist Takeuchi

Nasuverse: the overarching setting in which TYPE-MOON works usually take place, comprised of works written in settings created by Nasu. specifics vary heavily depending on timeline, but characters are often shared, along with the rules of how magecraft and magic work

Fate (originally just Fate/stay night): a popular urban fantasy visual novel that spawned a long-running media franchise. as distinguished from Tsukihime (an earlier visual novel by Nasu with its own timeline), Fate is kind of to Tsukihime what Persona is to Shin Megami Tensei

[Fate/Tsukihime] Worlds: a loose way of categorising the basic establishing events of a timeline. in Fate worlds, vampires are a much less organised threat and battle royales are held between mages in a desperate attempt to touch divinity. in Tsukihime worlds, the Dead Apostle Ancestors (primordial vampires) remain an ever-present threat and "servants" (heroic spirits summoned to fight in battle royales) do not exist. the latter worlds usually have a less hopeful tone, but both get really dark

Fate stories usually range from shounen to seinen that feels like shounen, while Tsukihime stories are more often distinctly seinen