Hello ethanlooo
You are mistaken.
The Swiss Half Fare Card is valid for the entire Swiss public transportation network, and this regardless of the operator. So, in a nutshell, the Swiss Half Fare Card is valid in Geneva, too. You can find its validity map here: Swiss Half Fare Card – Switzerland at half the price | SBB → Downloads.
Some mountain railways, gondolas, and funiculars do not accept the Swiss Half Fare Card, however. And, the Swiss Half Fare Card and the Trial Half Fare Card are two different products; the first is for tourists, the second for residents. The range of validity is the same.
Kind regards,
Roland