What's the difference between an IRA and a 401(k)?

A 401(k) is an employer-sponsored plan. That means that it is a benefit provided by an employer to employees, and allows the employee to divert some of his salary into it. That portion will not be considered part of the employee's taxable income. In other words, that employee earned a lower salary than he really did for the purpose of calculating taxable income. The portion of salary that got diverted into the 401(k) goes into an account that gets invested in different ways, usually into mutual funds. Those investments grow on a tax-deferred basis, meaning that the year-by-year growth of the investments is also not added to anyone's taxable income. It only becomes taxable when it is withdrawn. Most employers will throw in a contribution to their employees' 401(k) accounts as an added benefit, by matching employees' contributions dollar for dollar, up to a point.

An IRA has almost nothing to do with your job. It's set up by you and no one makes the decisions about how it is invested except you (unless you authorize a financial advisor to manage it for you). What makes an IRA special is the fact that the government agrees to give favorable tax treatment to your contributions and/or to the growth that accrues in the investment. This favorable treatment is long and complex in its details; there are Traditional IRAs and ROTH IRAs and there are a zillion ifs and buts about different situations.

How they are similar: They are both tax shelters for retirement investing.
How they are different: One is a benefit at work and managed by a contractor called a custodian (employer-sponsored) and the other is totally up to you to create and manage (self-directed).

Having both at the same time is possible but iffy. Check with an advisor who knows you and the particulars of your financial life if you want to get into that. There are no decent get-rich-quick schemes but these are good get-rich-slow schemes, so have at it and good luck.

I would also like to know

your mom