Question about ethics and possible misappropriation of research funds
I cannot really tell what you question is about, but let me try and clarify a few things.

First, being the PI on an institutional review board application does not make you the PI for the funded project. It is not clear what you mean by "your" project funds, but from your description it does not sound like it is your funding, but rather funding that your supervisor was awarded and is providing you access to for you to accomplish your thesis.

Second, applications for funding generally have around 3 aims. The linkage between these aims can be pretty loose. It is not uncommon for students working on different aims of the same grant to think their projects are completely independent. Often a grant might not provide funding for all the staff required to complete the aims. In fact a selling point to potential funders is the ability to leverage their funding with "outside" funds like a departmental studentship.

The real issue I think in your question is if it is ethical for your supervisor to use her funding to pay PhD students different amount. The answer to this is that it is most likely ethical. It is possible your supervisor has circumvented the policies of both the funder and the department, but this seems unlikely. It is quite likely that your department has a fixed, relatively low, stipend for internally funded PhD students, but allows for PhD students funded from outside grants to be paid more. In my mind there is nothing unethical about that.

So then the question is why is your lab mate being funded by the grant while you are being funded by the school. No one but your supervisor can answer this. Maybe she flipped a coin. Maybe she thought your the project of your lab mate was closer aligned to the aims of the grant. Maybe, as you say, she likes your lab mate better and cannot be trusted. Before going down that road, you need to remember that it is quite possible that the decision of who to fund from where may have been made prior to either of you applying to grad school.