Whether or not you have a 401(k) or a 403(b) retirement plan, you can also set up an IRA and contribute money to it. The limit on annual contributions to an IRA in 2020 is $6,000. If you make less than $63,000 per year as an individual, you receive a tax deduction for your contribution. As with a 401(k), you pay no taxes on the IRA or its investment returns until you retire.
A Roth IRA is an alternative to the traditional IRA. The money you put into a Roth IRA is taxed as regular income when you contribute it. Actually, since it probably comes from your paycheck, you already paid taxes on it. However, the investment returns are not taxed and the withdrawals (after age 59) are not taxed (unlike withdrawals from 401(k)s and 403(b)s. The logic behind setting up a Roth IRA instead of a regular IRA has to do with your perception of where tax rates will be in the future. If you think income tax rates years from now will be more than income tax rates now, then you would set up a Roth IRA. Finally, Roth IRAs are not allowed for people whose income is above certain limits.
Do not let all of this taxation rate talk confuse you. The fact remains that the IRS will tax you now or tax you later. For the 401(k) and 403(b), you are not taxed on the money now but are taxed on it when you withdraw it. For Roth IRAs you are taxed on the money now but not when you withdraw it.
Finally, there are certain IRS rules on required withdrawals at age 70 or 72 from 401(k)s. 403(b)s, and IRAs. This assures that the IRS gets their share if you have not yet paid taxes on it. You should get the advice of your tax accountant on IRAs. However, generally for a young person a regular IRA makes better financial sense than a Roth IRA.