Yes, they are. Back around the time when the game was first released, green bordered cards were called Magic Cards. However this term is actually a trademark belonging to Wizards of the Coast, publisher of Magic the Gathering. Since both products are a similar nature, this infringed on the trademark, so Konami changed Magic Card to Spell Card, then Magic Ruler to Spell Ruler.
In game terms, Magic Card and Spell Card are totally interchangable, different names for the same thing. If something instructs you to affect a Magic Card, it will apply to Spell Cards too, and vice versa.
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'Magic Cancellation' is the literal Japanese name for the video game-only card known as Cursebreaker in English. Despite having an almost identical picture to the genuine spell card De-Spell, the two cards are not the same thing. De-Spell is a Normal Spell card that destroys one Spell Card on the field, Cursebreaker is a Quickplay that negates other spell card activations on the same chain.
Quick-play Spell cards are Spell Speed 2, so are the same speed as all Trap cards except for Counter Trap cards which are Spell Speed 3.
It depends on what type of starter deck e.g. Yugioh 5ds, Yugioh GX, Yugioh!
'Sacrifice' doesn't appear anywhere in the English version of the game, it is a Magic the Gathering term here. But it is used in the Japanese version of the game, and is indeed the same thing as a Tribute.
Yes, it means exactly the same name, not anything that might contain the first card's full name. So something looking for cards with the same name as 'Yubel' would not search for 'Yubel - Ultimate Nightmare'.