A regular 401k is pre-tax like a regular IRA. There's also a roth 401k, but it's rarer.

If you have a 401k available to you, whether to invest in a traditional or roth IRA becomes more complicated, because the 401k also impacts your tax situation.

If after investing in the 401k, the roth math works out better, you can certainly choose the roth IRA over the traditional IRA for extra investments.

If you see the examples I posted in the other comment, if the 401k reduces your taxes, but doesn't remove you from the situation where the trad. IRA works out better, it could still be a better choice in the long run than the roth IRA - you really have to do the math to figure out which is the best option.

One of the biggest reasons you might invest in a 401k and a traditional IRA, is that if you can actually afford to put that much money aside (Combined max contribution is $25,000), there's a good chance you make too much money to put any money into a roth IRA. A single person earning $137k or more per year can not contribute to a roth IRA, but can contribute to a traditional IRA if they want the extra retirement investment. (The amount you can contribute starts to taper off at $122k. For married filing jointly, the limits are $193k starts to taper and $203k or more makes you ineligible for roth IRA)