I paid off my first mortgage but now have a second mortgage. The house is not worth the second mortgage and have no idea why they called it a second mortgage when the first mortgage was paid off when I got the second mortgage. Which bankruptcy (7 or 13)would be best if I want them to take the home. The home was never worth the amount of the refinance(or second mortgage). I need to start my life over some where else and having this home is stressful.

You could file either chapter, based upon what you have said so far. You can complete the Chapter 7 in about six months; the minimum time in a Chapter 13 is three years, unless the debtor has completed his plan beforehand. See: Chapter 13 - Bankruptcy Basics (http://www.uscourts.gov/bankruptcycourts/bankruptcybasics/chapter13.html) and the Chapter 7 link on the left margin.

A lot depends on your other debts and what other property you own.

In a 13 you normally are trying to keep your property and will work out a payment plan though the courts, but you can let your house go and work out payments on cars and credit cards

In a 7 you discharge your debts without making any payments, if you have a car you can re-affirm that debt and pay it at the regular terms

I paid off my first mortgage but now have a second mortgage. The house is not worth the second mortgage and have no idea why they called it a second mortgage when the first mortgage was paid off when I got the second mortgage. Which bankruptcy (7 or 13)would be best if I want them to take the home. The home was never worth the amount of the refinance(or second mortgage). I need to start my life over some where else and having this home is stressful.

If you want to remove your second mortgage, I would file for Chapter 13 bankruptcy. Chapter 13 is just a repayment plan so if you owe more on the first than what the property's worth you can file to "strip" your mortgage of its lien on the house and pay less money than if it was a secured debt

Src: The Law Office of Gene Turnwald - Bankruptcy Articles: Utilizing Bankruptcy to Remove Your Second Mortgage | Bankruptcy Attorney in Lansing, Michigan. (http://bankruptcylansingmi.com/utilizing-bankruptcy-remove-second-mortgage/)