401k is employer, IRA is individual.
Traditional contributions are pre-tax and tax deductible, Roth contributions are made with after tax money (i.e. you already paid taxes on your contribution. The contribution itself isn’t taxed.)
You can have any combination of these. Traditional or Roth 401ks (if your employer offers them), and traditional or Roth IRAs.
To put numbers to poobly’s answer, in 2018 you are allowed to contribute 5,500 to an IRA (total between traditional and Roth; if you contribute 4,000 to a Roth IRA and 1,500 to a traditional IRA, that’s your max of 5,500.)
IRAs have limitations.
Traditional IRA contributions are tax deductible (they lower your taxable income.) Below a certain income level, contributions are deductible dollar for dollar. Within a certain income range, contributions only give you a partial deduction (I’m not sure how this is calculated.) Above a certain income level, you can’t deduct traditional contributions at all. Regardless of income level, you can contribute to a traditional IRA, however, if your income is high enough that you can’t take a deduction, don’t contribute, or do, and roll it over to a Roth IRA.
Roth IRA contributions themselves are limited based on income level. Below a certain income level, you can contribute up to 5,500. Within a certain range, you can contribute something, but less than the max (not sure how that amount is calculated), and above a certain income level, you can’t contribute at all.
Side note, if you’re at an income level where you can only make partial or no contributions to a Roth, then you also can’t claim any deduction for a traditional IRA contribution. Max your traditional IRA, and in the same year roll it over to a Roth IRA. That protects your withdrawals/distributions from taxes in the future. Read here for specific numbers based on your filing status.
Traditional and Roth 401k’s might have their own limitations. I dunno. Too tired to look it up. For 401k’s in general, you can contribute up to 18,500 in 2018. If your employer matches your contributions, those employer match amounts don’t count against your 18,500 limit. (Employers match differently, so check with your employer. For example, an employer might match 50% of up to 5% of your pay period salary.) The absolute max that can be contributed through any means to your 401k account for 2018 is 55,000. So, if you contribute 18,500, and your employer matched all of it, that’s 37,000, meaning you could contribute 18,000 still. But your max is 18,500. What do? Make after-tax contributions to your traditional 401k (if your employer allows it.) The growth on that amount is tax-deferred (pay taxes on withdrawals.) Then you roll the after-tax portion into a Roth IRA, which makes the growth completely tax free, and withdrawals tax free (you already paid taxes on this amount when the contribution was made, it’s an ‘after-tax contribution.)
I don’t necessarily have my head wrapped around all that 401k stuff though because I’m not rich so I don’t need to worry about it. This ended up longer than I thought it would.