Refinancing will involve paying for appraisal, title report, escrow & other lending fees. You will need to be in an equity position on your home (in most cases) and credit worthy. You can refinance with your current lender or any lender you choose.
A loan modification is done with your current lender. You request that your rate and in some cases loan balance be modified to reflect the actual value, assuming its gone down and your ability to afford the home. Loan modifications are typically done when someone does not have equity and is having difficulty maintaining their payments due to a hardship.