Hi kendo
The lender offered you a rate and you accepted it. It shouldn't matter what that rate was called.
However, I suspect that your contract is for a home loan at the home loan tracker rate. It's not that they offered you the wrong rate, I suspect that they put you on a rate different to that which was on your contract.
Why did you choose the variable rate over the tracker rate? I would imagine that they intentionally had the variable rate below the tracker rate to induce you to take the variable rate.
The next question is which lender is it?
If it's ptsb, you should notify the Central Bank of this issue. They won't get back to you but they might investigate it as they are investigating ptsb's behaviour at the moment.
The difference between tracker and variable is so high and all the lenders are exploiting customers on variable rates, that I think you should complain to the Ombudsman.
Contact Padraic Kissane who specialises in this area. He will review your case and not charge you if he thinks you have no case.
Brendan