There is a difference. Some of the differences favor defined benefit, some 401k. If you have a 401k, it is your money. You can do with it as you will. In 30 years, I have personally paid over 100k into my defined plan. I can't touch a dime of that. If you have a 401k you can borrow against it and you can choose the vehicle of investment.
Most of the problems with governmental defined benefit plans have arisen from the failure of governments to put their share into the plan and trusting unrealistic market gains to make up the difference. That bill has come due.
I could be corrected on this but I'm 99.9% certain this is how it works.
- Pension Plans - Employee does not pay in. The company / entity has agreed to a "fixed" contribution per each employee. They can state the amount that must be contributed or they can define how much each employee gets at retirement (Thus the term Defined Benefit) NOTE: This is the nasty plan that kills entities because they have "0" flexibility. Once they've been established they cannot be cancelled which is to protect the employee.
- Profit Sharing - These are electable contributions. On a good year a company / entity, can determine how much or little they wish to contribute. With a 401K, the company match is an electable expense. The company has flexibility which makes it desirable to businesses. Today these plans are vastly more popular. Pensions are a thing of the past.
Of course this is a very simple explanation as there are many vesting rules, options, etc.