Does contributing to an FHSA reduce my income tax the same way an RRSP contribution does?

Yes, in the same general way. Contributing to an FHSA generates a deduction against your taxable income for the year, just like an RRSP contribution does, which means an FHSA contribution can genuinely lower your tax bill in the year you make it, not just when you eventually withdraw the money.

The key difference is that FHSA room and RRSP room are separate and don't compete with each other - contributing to your FHSA doesn't use up your RRSP room, and vice versa, so you can potentially claim deductions from both in the same year if you have room and cash available in both. Each account also has its own annual and lifetime limits set out in the Income Tax Act, so maximizing the deduction from one doesn't tell you anything about how much room remains in the other. Where the FHSA differs meaningfully from the RRSP is on the way out: a qualifying FHSA withdrawal for a first home is entirely tax-free, while an ordinary RRSP withdrawal is generally taxable unless you're using the separate Home Buyers' Plan. Coordinating contributions to both accounts based on your income and savings goals for the year is usually the more effective approach than treating them as competing choices.