There's no gradient on the string- it should have a uniform tension across it from nut to bridge (it might bind and be slightly different on the outsides ... which is why some guitars tend to go out of tune when you bend notes). As soon as you fret a note you shorten the string length. Pressure from your finger bending the string over the fret adds tension (why notes can go sharp if you press too hard). But again, it will be exactly the same on guitars with the same scale length & strings.
What you're describing is 'playability' (or other term to describe why it feels easier to play)- it's easier to fret and bend notes on a guitar with low action, a low nut and the bridge set up a particular way. But that doesn't change the tension of a given string.
If you decrease the tension on a string (loosen it), the note goes flat.



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