The X-Files were a special department, working within but somewhat separate from the FBI, concentrating on cases involving paranormal phenomena.
Agents of S.H.I.E.L.D will follow a special team, working within but somewhat separate from S.H.I.E.L.D, concentrating on cases involving superhero phenomena.
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Scully was initially a sceptic assigned to the X-Files, but gradually learns the truth.
From the trailer it seems Agent Grant Ward is assigned to the group, gradually learning more as the series progresses.
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The Lone Gunmen were a group of "geeky" investigators obsessed with conspiracy theories and the shadow organizations that they believe exist within the government. They also ran a conspiracy theory magazine.
Skye is a "geeky" investigator obsessed with superhero culture and the shadow organizations that exists within it. She also runs a conspiracy theory website.
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The X-Files produced two spin-off films.
Agents of SHIELD is spun off from a series of films, and is likely to have links to upcoming MCU films
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Wikipedia says “In addition to the series-spanning story arc, "Monster-of-the-Week" episodes formed roughly two-thirds of the episodes. In such stand-alone episodes, Mulder and Scully investigated strange crimes that had no effect on the show's mythology, though the episodes enriched the show's background”.
This will surely be the format that Agents of S.H.I.E.L.D will take...