Yes, there sure is a difference...
The "Erase all data and settings" does exactly that - all of your personal data, apps, settings, etc are zapped permanently and the operating system is reinstalled. This makes your phone as though you just took it "out of the box" new. You MUST do this before you give an old phone to someone else.
HOWEVER, before you do an "Erase all data and settings", make SURE you back up your phone either to iCloud (found in the phone's settings) or by cable to iTunes on your computer. When you get your NEW phone and activate it, you plug your new phone into iTunes and it restores everything you had on your old phone in a few minutes - all apps, settings, data. An iCloud restore will do the same thing, but not as fast as iTunes.
