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A traditional IRA is tax free going in, but taxed coming out. A Roth is the opposite and taxed going in, but tax free coming out.
Mathematically, they're equivalent. The only reason to choose one over the other is your personal income tax rate. If you think you'll pay a lower tax rate in retirement (because you won't be making as much, and thus will be in a lower tax bracket), then you'd pick a standard IRA. If you have a shit job now and expect to make more later, a Roth would make more sense.
You're correct about the now vs. later part but I'll also note that tax laws can change and some people think that getting ahead of the curve and confirming their taxes now via Roth has value. I'm not one of them, but it's certainly a strategy.
The only reason to use a Traditional IRA and not a normal brokerage account is so you can backdoor it into a Roth IRA. Since you can't make Roth IRA contributions when you are above a certain income limit, but you can roll over a Traditional IRA into a Roth IRA, this let's you avoid taxes on the growth of the account.
This is the real answer to the question given the nuance in the question of “if you make a lot”
As I understand it, the interest income is tax deferred while it is still in the IRA. So over a long period it can appreciate a lot more than if taxes were being taken out every year.
My understanding of this (just worked through it with my wife) is that you will not take a tax hit on the disbursement when you take it but you will get hit with capitol gains taxes on it's growth from inception of your contributions.
When you take it out, it has already been taxed but it will still count as income for your tax planning purposes in the year you receive it - hopefully you're in a lower tax bracket when this occurs. It is not a taxable income (though it counts as an income and increases your tax bracket accordingly) but it's growth since contribution will cost you at your current tax bracket as you take it.
Not a financial wizard here, ask a professional.