You are replacing your old loan with an entirely new one with different interest rate and terms.  Your new mortgage may come from the same lender or another. Since the  new loan pays off your old mortgage it doesnt much matter whether you change lenders in a refinance.

Most borrowers choose to refinance their mortgage to take advantage of lower interest rates, consolidate higher (non-deductible) interest rate debt, or to cash out equity in their home.

A rate and term refinance trades in your old mortgage(s) without raising the loan amount. You may be permitted to see some (minimal) cash at close. Usually the lesser of two percent (2%) of the new mortgage amount or $2,000. 

When consolodating mortgage loans (1st, 2nd etc..), they must have been originated at the same time to qualify for a rate & term refinance.  If not, you may be able to exclude other mortgage loans to perform a rate & term refinance on your 1st mortgage loan alone.  

A cash-out refinance allows homeowners to tap the equity in their homes, (property value minus all mortgage liens) and the amount is limited only by the lenders maximum loan to value (LTV) caps for this program.  Because the new loan size is greater than before, lenders consider it higher risk and generaly charge higher rates for this loan type. 

Consolodating higher interest 2nd loans & variable rate home equity lines may still make sense as most 2nd loans have even higher rates reflecting the higher risk 2nd lien position represents to the lenders. I recommend my clients consider opening a new home equity line with their new 1st mortgage so they may be eligable to consolodate it as a rate & term refinance if needed later.

www.GregZaccagni.com & www.MortgageAdvisor.info