Most people think of IRAs as traditional or Roth. There are actually three types: deductible and nondeductible traditional IRAs and Roth IRAs. An IRA funded with money from a 401k or other qualified retirement plan may use "pretax" and "after tax" to describe deductible or Roth-type contributions. It's vital to keep careful records, as your later tax obligation depends on where the money came from in the first place.
The term "pretax" in IRAs usually refers to an IRA funded with money from a traditional 401k or other qualified retirement plan. "Pretax" refers to the fact that the 401k contributions come from your gross pay, before taxes. Pretax IRAs are equivalent to deductible traditional IRAs: you get to deduct the value of your IRA contribution from your taxable income. You do not pay tax on your pretax IRA contributions or any income you earn in the account until you withdraw it in retirement. These withdrawals are required -- you must take an IRS-prescribed minimum amount of money from your pretax IRA each year once you reach age 70 1/2.
The term "after tax" is tricky, because both nondeductible and Roth IRA types are after tax. Typically, however, this term is used to refer to nondeductible traditional IRAs, since "Roth" is such a specific term. Anyone can contribute to a traditional IRA, but the IRS limits the amount of those contributions you can deduct from your taxable income if your gross adjusted income goes over certain limits. The rules for an after-tax IRA are the same as for the pretax IRA, but in this case the only tax you defer is the tax on any income earned in the account.
If you have after-tax contributions in your 401k plan, it's most likely that these contributions are Roth-style contributions rather than after-tax traditional contributions. Like a nondeductible traditional IRA, Roth contributions are taxed before they go into the account. Unlike a traditional IRA, however, earnings on those contributions are never taxed, and you are not required to take withdrawals in retirement. The IRS limits Roth IRA contributions to those with incomes below a specific amount, but as of 2011 anyone can make contributions to Roth 401k plans -- and roll those contributions to a Roth IRA -- or convert a traditional IRA to a Roth.
The most crucial difference between the three IRA types is taxability. With a traditional IRA, you will pay tax on both your contributions and their earnings -- it's just a matter of when. With a Roth IRA you'll pay tax on your contributions but not on the income, provided you follow the IRS rules. Different income limits apply for each IRA type, and these change from time to time. Review your options with an accountant or financial planner to determine which option is best for you.