Legal Question in Bankruptcy in California

Winding up is only something businesses do so I'm going to answer in a business context.

Winding up is the process of stopping the business and disolving it.

Insolvency means you can't pay your debts.

Sometimes companies who are not doing good, i.e. insolvent, will file for Chapter 7 to close the company and not worry about certain ramifications of its debt.

Sometimes companies will file for Chapter 11, which allows them to restructure or get rid of some of their debts because the company makes money, but just not enough to pay all of its debts.