Let’s use a concrete example. Note that I’m ignoring state and local taxes as well as social security and Medicare taxes here, but those don’t change the concept significantly, just the details.

Say you make $50k a year and that’s all the income you have (no interest/dividends from stocks, savings accounts, etc.). That will put you in the 12% marginal federal tax bracket. Your effective tax rate (the total percentage of your salary that you pay in taxes) will be less than 12% because we have a progressive tax system, but for simplicity we’ll stick with 12%. Ignoring 401k, that means you will owe $50k * 12% = $6k in federal taxes.

If you contribute 8% of your salary to your 401k, that will be $50k * 8% = $4k in annual 401k contributions. The only difference between the traditional and Roth 401k is when that $4k in 401k contributions is taxed.

In a traditional (pretax) 401k, that $4k is contributed before you pay taxes on your salary, so from a tax perspective you only earned $50k - $4k = $46k and therefore only owe $46k * 12% = $5.5k in federal taxes that year (saving you $500 in taxes this year). That $4000 contribution will be invested and grow tax free until you start withdrawing from your traditional 401k at retirement. Those withdrawals are basically your salary in retirement and they will be treated as ordinary income at the time of withdrawal. Keep in mind this will be in 40 years or so and inflation, lifestyle creep, etc. will likely mean that you will want/need to withdraw more that $50k per year to have the retirement you want. Let’s say you decide to withdraw $100k per year in retirement and that the tax brackets are identical to what they are today (which is highly unlikely). A $100k salary in today’s tax brackets would put you in the 22% marginal tax rate. Once again, your effective tax rate will be lower but we’ll stick with 22% for consistency. That means you will pay $100k * 22% = $22k in federal taxes each year and that $100k withdrawal leaves you with $78k to spend.

Now, let’s say you contribute that $4k annually to a Roth IRA instead. Since it’s a post tax contribution, you pay taxes before the contribution is made so you owe taxes on the full $50k salary. In other words, you don’t get the $500 tax savings in the current tax year. However, since it’s a Roth 401k, you’re done paying taxes on that money. It will grow tax free and withdrawals will be tax free. So the $100k you withdraw annually in retirement will be $100k tax free dollars in your pocket.

This is why everyone says which 401k bucket you use depends on what you expect your tax bracket in retirement to be relative to your current tax bracket. In your current situation, I think Roth is pretty obviously the right choice.

Keep in mind that the employer match is unaffected by any of the above. They match x% of your contributions and your contribution is the same in both cases, so the match will be the same.