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To have Swiftness (X) is to be X% faster than normal.
This only affects Combat Speed; that is, how fast you can run in battle. Your other movements aren't boosted similarly, or at least aren't controllable enough to be useful in combat or anything else.
This is not to be confused with Quickness, which provides more useful speed but is quite exhausting.
Swiftness is a buff shared between Nature and Air:
For stacking purposes, you should know that the three spells do NOT stack with themselves or each other.