Canada never used to have a "pay tax now, but don't pay tax later" investment option, until 2009 when the TFSA (Tax-Free Savings Account) was created. Is this fundamentally the same as a US Roth IRA? e.g. can I read American investment advice and mentally substitute "TFSA" when I read about IRAs? Is there any subtle difference I should be aware of?
The closest American thing to Canadian TFSA were the Lifetime Savings Accounts (LSA) proposed during the first term of George W. Bush administration. LSA had many features of TFSA: after-tax contributions with an annual limit, tax-sheltered growth, tax-free withdrawals of both contributions and earnings at any time.
(The proposal was never enacted - here's a politically-neutral explanation: LSA amounted to a tax cut on investment income and, considering the cost of tax cuts of 2001 and 2003 and two wars, it was very difficult for the Congress to pass such a proposal.)
Without LSA, Roth IRA is the closest thing. There is one important difference. From Roth IRA, you can only withdraw contributions in nominal dollars, not adjusted for inflation. Earnings can be withdrawn without penalty only in retirement. This condition makes Roth IRA suitable primarily for retirement savings.
TFSA, due to their tax-free withdrawals, are suitable for saving and investment of any time horizon, from long-term retirement investing to saving for the next major purchase (car, appliances, or home improvement).
The fundamental idea is the same, so most of the time you can read "TFSA" when someone writes "Roth IRA," particularly when the topic is which option is a more tax efficient option in the long term.
However, the TFSA is more flexible, and it may be appropriate to use in cases where a Roth IRA is not. When you withdraw money from a TFSA, you regain your contribution room the next year. I believe this is not the case with the Roth IRA. Also, unused contribution room in the TFSA carries forward, while it does not with the Roth IRA. I also believe there are some rules about Roth IRA contributions having to stay invested for 5 years before the earnings can be withdrawn tax-free, but I'm not too sure on the details of that. Either way, there is not restriction in the TFSA.
I believe you also have to be making income to qualify for contributing to a ROTH IRA and income that you have paid tax on through the year. US schemes alway seem to involve an employee i.e. the power to allow these things to flow through an employer in some way.