Baba Kama 33a - Calculating half damages of Tam

The Rosh understands from rashi that the calculation of "chatzi nezek" in case where a Tam and Mu'ad damage each other, is to consider the difference to be the damage and pay half of the difference. For example, if the damage of the tam to the mu'ad is $200, and the damage of the mu'ad to the tam is $150, since the net damage to the mu'ad is $50, the tam pays half of that which is $25. Or for example, if the damage of the tam to the mu'ad is $200, and the damage of the mu'ad to the tam is $50, the difference is $150, of which the tam pays only half which is $75. The Rosh is medayek from Tosafos who considers the entire mishna (except for the opinion of R' Akiva) to be superfluous, that they assume we calculate so that the tam will only be liable for half the damage that it caused. Therefore, in the first example we divide the $200 in half so that the liability of the tam for the mu'ad is only $100, and the liability of the mu'ad to the tam is $150 so that the mu'ad has to pay the tam. Also, in the second case the liability on tam for mu'ad is $100, and mu'ad for tam is $50 so the tam will only have to pay $50. See the nimukei yosef brings different possibilities of how to calculate.

Tosafos seems to be correct. Since a tam only pays half, we should consider the damage the tam did to the mu'ad to be half of what it actually is, and only then calculate the difference in damage. Why does rashi consider the damage to be the difference?

It seems that there is a fundamental question in the concept of chatzi nezek for a tam. Is chatzi nezek a din in how we view the damage (i.e. half of what it was), or is it a din in the payment (it is always reduced by half)? Tosafos holds that chazi nezek is a din in the damage, that we value the damage as half of what it actually was. Therefore, when a Tam causes $200 worth of damage, we view it as it only damaged $100 worth. But rashi understands that the damage is viewed in full, but regarding the payment, a Tam only pays half of what he owes. Therefore, we figure out the net damage that the tam owes the mu'ad and then divide it in half.