In 3.5, yes, the character does. Difficult to prove a negative, but quite simply, nothing says they don’t. And the penalties do not share a type.1
- Penalties aren’t really supposed to be typed in the first place, actually. The rules are unclear what you do with them when they happen. Nonetheless, a few typed penalties do exist; I recommend simply ignoring the types in such cases as they should have been removed during editing and their publication was in error.
In Pathfinder, however, the wording states “base land speed” in reference to taking penalties.
Base land speed is your unencumbered speed. Base land speed is calculated by applying all modifiers to your character’s speed with the exception of armor or encumbrance adjustments or any effect that modifies your “normal speed”.
So armor slowing you down wouldn’t count as part of your base land speed, and thus would not resulting in penalties to Acrobatics checks made to jump.