The main difference is the type of employers who can offer them. Unlike 401(k) plans which are offered by for-profit companies, 403(b) plans are only available to employees of tax-exempt organizations. These are usually either schools, hospitals or religious groups. The names simply refer to the section of the tax code that outlines these plans.
For the most part, the two types of plans work the same way. But there are other subtle differences. For example, 403(b) plans will sometimes offer more limited investments choices than corporate plans, which might consist of annuity contracts and mutual funds. But that may change due to new regulations set to go into effect in 2009, which aim to make 403(b)s even more like 401(k)s. While 401(k)s frequently have vesting schedules spread out over a few years, many 403(b)s vest immediately, or over a shorter period of time than in their cousins in the for-profit world.