I'll give you the thumbnail version of the main difference between the Traditional IRA and Roth IRA.
In the TIRA, you get a tax deduction for what you contribute, your investments grow tax free, and when you pull the money out, you pay taxes on it.
In the RIRA, you put money that's already been taxed into the account, but when you pull it out, it's tax free.
Lots of other nuances, but that's the difference that most people focus on. The thing is, if you make enough money, you're phased out some of the benefits of each. For a RIRA, the phaseout of what you can contribute (if you're under 50 and single) is from $110,001 and $125.000. For a TIRA, there's no income cap limiting what you can contribute but
as you earn more, the amount of that contribution that you can deduct limited
if you are covered by a retirement plan at work.
For years, I was pretty much ineligible for contributing to a RIRA and phased out of getting a deduction for a TIRA. So I made contributions to a non-deductable TIRA instead (tax-free growth is better than nothing, even if you do have to pay taxes on the growth on your way out).
Then in 2010 (and this situation is allowable through this year), we were allowed to convert TIRAs in to RIRAs. The catch was that you had to pay back taxes what you'd deducted in previous years and also pay taxes on the growth in those years. So what you can do pay into a non-deductable TIRA and convert immediately to a RIRA. When I did that this year, I only had to pay taxes of a few dollars because it took 2 working days to do the conversion and my $5K had grown in value during those 2 days, so I had to pay taxes on that small amount of growth.
Hope that helps. Vanguard can definitely explain to you in greater detail.