Whoa. These things are on two dimensions. It's like burger and fries, you can also have chicken sandwich and fries, or burger and onion rings.
You can invest in an taxable brokerage account and/or an IRA.
And then, within each of those...
You can buy index funds and/or anything else.
All 4 combinations are possible.
If someone says otherwise, take your money and run. They are a shady financial "advisor" who is ripping you off by steering you only into products where they get a commission. Those products are more expensive because the commission comes out of your end. Not to mention any names. E.J.
If you want financial advice that is honest, find a financial advisor who you pay for his advice, and who doesn't sell products at all. Or, just ask here.
But I would start by listening to Suze Orman, Dave Ramsey, whomever you prefer. And read John Bogle's book.
They can tell you all about the difference between money market, bonds, stocks, managed mutual funds (ripoff!) and index funds.
IRA accounts, Roth IRA accounts and taxable accounts are all brokerage accounts. Within them, you can buy any security you want, including index funds. The difference is taxation.
Suppose you earn $1000 and choose to invest it however Later you withdraw it and it has grown to $3000.
Investing in a taxable account, you pay normal income tax on the $1000. When you later withdraw the $3000, you pay a tax on $2000 of income. If you invested more than a year, it is taxed at a much lower "capital gains" tax rate.
With a traditional IRA account, you pay zero taxes on the initial $1000. Later, when you take the money out, you pay normal income tax on the full $3000. If you withdrew it before age 59-1/2, you also pay a 10% penalty ($300).
With a Roth IRA account, you pay normal income tax on the $1000. When you withdraw the $3000 later, you pay NOTHING in taxes. Provided you followed the rules.
You can invest in almost anything inside these accounts:
Money market funds. Terrible return. You won't keep up with the
Bonds. Low return but usually quite safe.
Individual stocks. Good luck.
Managed mutual funds. You're paying some genius stock picker to select high performing stocks. He has a huge staff of researchers and good social connections. He also charges you 1.5% per year overhead as an "expense ratio", which is a total loss to you. The fact is, he can usually pick stocks better than a monkey throwing darts. But he's not 1.5% better!
Index funds. These just shrug and buy every stock on the market. There's no huge staff or genius manager, just some intern making small adjustments every week. As such, the expense ratio is extremely small, like 0.1%.
If any of these investments pay dividends, you must pay taxes on them when they're issued, if you're not in an IRA account. This problem gets fixed in ETF's.
Index ETF's. These are index funds packaged to behave like stocks. Dividends increase your stock's value instead of being paid out to you, which simplifies your taxes. If you buy index funds outside of an IRA, use these.
Too many other options to get into here.