If you want to change the type as you make the transfer, you can owe tax. For example, a Traditional 401(k) where you want a Roth IRA would be taxed, as you experienced before. But starting with a Roth IRA, you will keep it intact as a Roth IRA, and no tax would be due.
In the future if you have a Traditional 401(k) and convert it to a Roth IRA, it's added to your income. So if you convert $10,000 then you owe tax on $10,000 worth of additional income. So on your tax form you might have the median salary of $52,000 and the conversion would mean you pay tax on $52k + $10k = $62,000.