The differences are all about tax deferment. Traditional IRA and 401k accounts allow you to defer paying income tax on the money you place in the account, and defer paying income tax on the earnings within the account (allowing the money to grow larger, since you don't have to use some of the money to pay those deferred taxes). In exchange for this, you must pay taxes when you withdraw from the account, at normal income tax rates.
Roth and taxable accounts don't receive any immediate income tax break, but in a Roth IRA (or Roth 401k) the money in the account grows tax free and is tax free when you withdraw it (you paid the tax upfront). Dividends and capital gains (if you sell stocks, etc) in taxable accounts are taxable each year, but at preferential rates vs. normal income rates, possibly zero.
There can be other reasons to use certain types of accounts. If your employer has any kind of a 401k match, you should at least put in the minimum required to get the match - that is free money. We personally put as much as we can in DH's 401k to lower our AGI to capture as much EIC as we can, especially since NYS matches EIC at 30%. We then turn around and use that tax refund to fund our Roths, so it is tax free going in and coming out!