Both 401(k) and Roth 401(k) grow tax free. Any dividends or capital gains paid out by your investments, or gains you have from trading inside the account, are not taxed. If you take money out of these accounts too soon, though, you will have to pay taxes and penalties. The below assumes you leave the money in the account until retirement age and only make allowable withdrawls.
With a traditional (non-Roth) account, however, withdrawals are taxed - and they are taxed as ordinary income. The entire amount you withdraw is subject to tax. So if you withdrew the entire $100k all at once, you would pay tax on all of it. If you only withdraw a little bit, you only pay taxes on that. It gets counted with all your other income for tax purposes. If you have a high income while you withdraw, you'll pay a higher tax. If you have little or no other income, you will pay a much lower rate (possibly 0, if the total amount subject to tax is below the standard deduction).
With a Roth account, you pay taxes on the money now, at your current income tax rate. Then you are done paying taxes on this money. Withdrawals, unlike in the non-Roth case, are not subject to tax. You could withdraw the entire $100k at once if you wanted without having to pay tax. However, if you then leave it to grow in a non-tax-advantaged account, you'll have to pay taxes on dividends and gains, so you should only withdraw money you actually need to use.
Note that in the non-Roth case, when the tax is levied (on withdrawal), you are receiving the money that is being taxed, and can use it to pay the tax. In the Roth case, the money is subject to tax when it goes into the account; you need to have other cash on hand available to pay the tax that year.