In the most basic of terms, your 401(k) is a plan you participate in controlled by your employer with set specific investment options. You do not "own" the money. In an IRA you own the money and generally have a much broader selection of investment options and the ability to get professional advice. Also, the contribution limits are different. Both allow for "catch up" contributions for those over age 50+, but the amount you can contribute to an IRA for catch up or tax deferral is much less than what is allowed in 401(K).
Here is a helpful link on recent changes to contribution and income limitations for 401k and IRA