Well... let's first look at some game sequels in the past, and compare them.
Might and Magic... same general gameplay mechanics, unrelated stories, different worlds, similiar appearance (artistically).
Final Fantasy... same general gameplay mechanics, unrelated stories, same universe/different worlds, similiar appearance.
TES... continued lore, mention of past events, same continent, slightly differing appearance in places.
Grandia... same general gameplay mechanics, unrelated stories, same universe/different worlds, similiar appearance.
AD&D Dragonlance Silver Box series... continued storylines, varying degrees of similiarity in gameplay, same locale in the same universe, dealing with literary heroes, similiar appearance in stills/various appearances in gameplay.
Phantasy Star & PSO... same gameplay mechanics, same storyline, nods to previous notable characters, same universe/different worlds, similiar appearance.
Warcraft... same genre, same appearance, same gamplay, same universe.
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Now, let's look at some spin-offs and see what differs
TES: Adventures... same continent, same lore, differing gameplay style, differing gameplay mechanics, generally differing appearance
FF Tactics... vastly different gameplay, different storyline, same universe/different world, similiar appearance.
FFX2... a continued storyline from a previous game (and hence, makes it a spin-off, since the series is defined by being non-sequels)
Grandia Tactics... vastly different gameplay, different storyline, same universe/different world, similiar appearance.
PSO: CARD Revolution... similar in concept, yet vastly different in execution, of gameplay mechanics; same storyline; nods to previous notable characters; same universe/different worlds, similiar appearance.
Heroes of Might and Magic... different gameplay, different storylines (I believe), different worlds (I believe) [someone correct me if I'm wrong], somewhat different appearance.
AD&D Dragonlance Gold Box series... same (or similiar) gameplay mechanics to each other (but vastly differing from the Silver Box games), related stories to each other (but long after the events of the Silver Box games), same locales within a given universe, dealing with PC heroes, similiar or differing appearance in stills/differing appearance in gameplay.
World of Warcraft... different genre, same appearance, different gamplay, same universe.
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Reflecting upon that, I see that previous games always kept a majority of elements consistant within the series, and only the most defining traits remained consistant within the spin-off (to ensure that it is still 'feels part of that universe'), whether those main traits are gameplay style, main characters, setting, or whatnot.
So, with all that being said, let's look at FO1, 2, T, BoS, and 3...
1 and 2: Similiar gameplay, similiar appearance, continued storyline, similiar locales within a continent, continued lore, same genre.
Tactics: Slightly different combat gameplay, vastly different non-combat gameplay, similiar appearance, tangent storyline, different locales within a continent, continued lore, different genre.
BoS: Vastly different gameplay, vastly different appearance, tangent storyline, different locales within a continent, ignored lore, different genre.
3: Considerably different gameplay, considerably different appearance, possibly a tangent storyline (or, could remain true, only time will tell), different locales within a continent, possibly ignored lore (again, only time will tell on this point, but so far it's not looking good), different genre.
In light of previous games, I would say, that despite the fact that FO3 is numbered as a sequel, it's predecessors (both in the series, and historically) seem to point at the fact that it is, indeed, a spin-off.