That's fine information NewStachian, but I don't think you answered HAULIN's question.
The over-50 contribution limits you're referring to are $23,000 for a 401k and $6,500 for an IRA (each). 401k and IRA refer to the type of account, a 401k is an employer-sponsered retirement account, an IRA is an Individual Retirement Account that you open for yourself. Traditional and ROTH refer to when you will pay income tax on the money, in Traditional accounts (both 401ks and IRAs) you pay it on withdrawing the money, in ROTH accounts (both 401ks and IRAs) you pay it when you contribute the money.
Most 401k accounts are Traditional 401ks. So much so that it's assumed that when people are talking about 401ks they're talking about Traditional 401ks. Your 401k though has the option of allowing you to make contributions either as a Traditional or ROTH 401k. Regardless of which you choose (or you could do both), your contributions to your 401k will still count against your 401k limit of $23,000. In addition you can contribute to an IRA (or IRAs) (ROTH or Traditional or both) up to the IRA limit of $6,500.
As to which you should invest in first that's where NewStacian's post becomes helpful. If your tax rate is going to be lower in retirement than it is while you are working (true for almost everyone) then you should wait to pay income tax until you are withdrawing, aka you want to invest in Traditional accounts. If not then vice versa. As to the order of 401k vs IRA, order is generally 401k up to the company match (if any), IRA next so that you have complete control over what funds you can purchase, and then 401k again after IRA is maxed out. If you can max out both 401k and IRA contributions then order matters not at all.
The issue is further complicated by less visible IRS rules. For example, even though you can always *contribute* $6,500 to a Traditional IRA, you can only *deduct* the full amount from your taxes if you make below certain income limits (
http://www.irs.gov/Retirement-Plans/Plan-Participant,-Employee/2014--IRA-Contribution-and-Deduction-Limits---Effect-of-Modified-AGI-on-Deductible-Contributions-If-You-ARE-Covered-by-a-Retirement-Plan-at-Work ). If you make too much and can't deduct a Traditional IRA contribution, then there's very little point in making it in the first place; you'd be better of with a ROTH IRA. But ROTH IRAs have their own limits too, where if you make too much you simply can't contribute to them (
http://www.irs.gov/Retirement-Plans/Plan-Participant,-Employee/Amount-of-Roth-IRA-Contributions-That-You-Can-Make-for-2014 ). So in that case the really high-income people have to do silly things, like contribute to a non-deductable Traditional IRA and then convert it to a ROTH IRA. 401ks have the benefit of not being bound by these silly additional rules.
So anyway, it is complicated, it's not just you. Hopefully that helps clear things up more than it muddies them though.