Why should I open a traditional IRA or a roth IRA?

I am trying to learn about the IRA and roth IRA but I don’t understand where the benefits are?
In a traditional IRA income taxes are paid by distributions while by a roth IRA income taxes are paid by contributions.
I am not sure if capital gain taxes are paid or not by traditional and roth IRAs, would that be the benefit in investing in those retirement plans, avoiding capital gain taxes?
Where are taxes lower, in a traditional IRA or a roth IRA if I invest in a mutual fund that pays every year gains to investors (mutual funds have to sell securities that appreciate every year and share the gains with investors)?

In Roth and Traditional IRA’s your earnings are not taxed.

The difference is that for a traditional IRA your money goes in without any taxes coming out before hand. So if you put $4,000 in than you will deduct $4,000 from your total income that year and not get taxed on it. (Your tax would have been your tax rate x $4,000). When you take the money out in retirement you will be taxed regularly.

With Roth IRA’s your money goes in after tax. So, keeping everything the same, your $4,000 would get taxed by your tax rate which we will assume is 30%. So you will have $4,000 – $1,200 = $2,800 to put away. In retirement you WILL NOT have to pay taxes on the money which has grown.

So, a main argument for Rother versus regular has to do with wether you think taxes will be higher later in life than right now. Another strategy is to just diversify and invest in both regular IRA and ROTH.