The exact same string tuned to the exact same pitch across the exact same scale length requires
the exact same tension.
From the referred article:
T = (2Lf)
2μ
For the same string, μ is the same. If you're tuning to the same frequency, f is the same. If the string is stretched across the same scale length, L is the same. Therefore, the tension T is the same.
Bongomania is right on when stating that the reason for the difference in feel is due to the influences of the instrument. It
isn't the string tension, that's for sure. You could put that string up across a 34" pile of bricks and it'd have the same tension it has on your Lakland.