Roth 401k plans and normal 401k plans are retirement plans that are sponsored by your employer. Putting money in these plans allows it to grow tax-free as long as it remains in the account.
Contributions to a normal 401k plan are made with pre-tax dollars, which means that money is not taxed as income that year. Contributions to Roth 401k plans are made with after-tax dollars, meaning you have to pay taxes on the contributions as part of your income.
When you withdraw money from your normal 401k, you must report the money as income on your taxes. When you withdraw money from your Roth 401k, the money is taken out tax-free.
Matching contributions made by your employer for your contribution to a normal 401k can be added to that same account. Matching contributions made by your employer for your contributions to a Roth 401k must be put into a normal 401k.
When deciding which to invest in, you should generally choose the Roth 401k if you expect to fall in a higher tax bracket at retirement than you are in now because the savings you reap when you withdraw the money will outweigh the tax savings of contributing to a normal 401k.
The Roth 401k was introduced in 2006 while the normal 401k plan was introduced in 1978.