Another short answer to help you be unconfused
401k and ROTH 104k - come from your work, generally they put in some money when you put in some. Their account will have limited option in what you can buy. You can have many 401k accounts each from any jobs you have opened any with. There is a government limit of around 16k (i think) that you can put in every year.
IRA and ROTH IRA - TONS of places have IRA, vanguard, lendingclub, etrade, fidilty, tons and tons of places. You can only put in about 1/3rd of what you can than with a 401k, of only 5,500 each year. You can open up as many of these accounts as you like, on as many websites, but ONLY can put in that yearly max amount. If not uncle sam gunna be pissed.