What are “S-“ skills?

In each character skills I sometimes see “S-“ versions of skills, what are these verses the non “S-“ versions?
Example: “S-HP” vs “HP”, “S-Speed 1” vs “Speed 1”

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S- stands for ‘Super’, normally S-skill increases stats by a percentage

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What if I have both skill:
S-block
Block II

Are the benefiting rating and percentage stacks?

I have Magic Attack III and S-Magic Attack on my mage and it looks like the benefits do stack.