PMI and MIP insure the lender for any losses suffered if the borrower defaults on the payment. They are typically included in a monthly mortgage payment.
Private Mortgage Insurance (conventional loans): The lender cancels PMI when LTV (loan to value) reaches 78% or 22% equity in the property. Loan to value means the amount borrowed in proportion to the current market value (based on appraisal) of the property.
Mortgage Insurance Premium (FHA loans): As of June 3, 2013 all FHA loans have a 1.35% (of the loan amount) monthly mortgage insurance. However, unlike conventional loans, MIP remains for the life of the loan. To cancel the premium, the borrower must refinance the loan and have 20% equity in the property.
To recap: PMI can be canceled with enough equity in the home. MIP remains for the life of the loan regardless of equity.
Any other terms that confuse you? Let me know!
Photo courtesy of nikcname (Flickr)