The only difference is in the degree of formality expressed, not in the meaning as OP appears to have learned somewhere.
In the order of formality: 高くとも、高くても and 高くっても.
To speak of the meanings, there are TWO meanings in each form.
1) "Even though (something) is high, tall or expensive"
2) "At the highest, tallest, most expensive" It indicates the possible maximum height or price.
Example sentences:
1) 「Aブランドのラーメンはおいしいので、[高]{たか}くてもつい[買]{か}ってしまうね。」 つい = without meaning to
2) 「高くても[千円]{せんえん}[出]{だ}せばこの[町]{まち}のほとんどのレストランでお[昼]{ひる}が[食]{た}べられるよ。」 お昼 = lunch
EDIT: I think I now know what OP means by "fundamental difference in meaning". An older book or a strict grammarian might say that only とも should be used for meaning #2 above. In the real Japanese-speaking world of the 21st century, however, ても is probably used more often than とも in informal speech for #2.