The term "refinancing" is used in this web site to mean "replacing your existing mortgage" with a brand new one. Following is a menu of options to choose from:
 

Taking Out Equity From your Home ("Equity Take Out")

Larger than the existing one, but without blending in any other mortgages, in which case it is called an "equity take out", usually to consolidate non-mortgage debt, such as credit cards or loans, or to make improvements to your home.

Consolidating Existing Financing

Presumably to lower the total interest cost. Referred to as simply a "refinance".

Refinancing When you Can't Transfer to a New Lender

Held by a private, or little-known lender whose mortgages are not accepted for switch purposes by your new - presumably larger - lender (may be either increasing the balance, keeping it the same, or lowering it) . Also referred to as simply a "refinance".