Is converting a traditional IRA to a Roth IRA the same as opening a Roth IRA account and rolling over the money from the traditional IRA? Are they different in any way?
Yes, very. Opening a Roth - there is a limit of $5500 ($6500 if age 50 or older) for the year as well as a phaseout based on income, starting at $135K if single, $199K if married filing joint. Of course, this is for a new deposit, the choice is this or the conversion I discuss next...
Conversion - there is no income limit. Taxes are due on the amount converted, taxed in the year of the conversion. If any IRA money was not deducted, you add all IRA money and pro-rate the amount converted so it's not taxed twice.
Above numbers updated to reflect 2018 numbers and rules.
You cannot just transfer or rollover from a traditional to a Roth IRA, because they are taxed differently. You'd have to do a distribution from your traditional (which will be taxed and possibly penalized, depending on your income and age), and a contribution to your Roth (which is limited based on annual contributions to all your IRAs).
A conversion is not limited by dollar amount (unless you must take an RMD... required distributions may not be converted). There is no income limit for 2010 and beyond (previously $100k MAGI), and there are no penalties. However, all you must pay tax on all untaxed dollars - this means the original contributions as well as the growth.
It all depends on the size of your IRA, your investment options, and your expected tax bracket at retirement. Traditional IRA distributions are considered income for the year, while Roth distributions are not.