Contributed By: Cliff Hobbs [MVP ConfigMgr/ SMS]
There is actually more than one difference between the two methods. To explain:

Updating a Package

• Use it When: You've made actual changes to the actual Package source files such as adding, changing or removing a file(s) or directory.
• What it Does: Creates a new compressed version of the Package (and delta compressed Package file) from the updated source files. The delta is distributed out to all DPs (in other words this creates WAN traffic).
  • Doesn't reset the Access Control List (ACL).
  • Resets the Virtual Directory if BITS has been enabled or disabled on the DP since the last Package update.
  • Updates the Package Source version.
  • Increments the Package version in Client Policy.

Refreshing a Package

• Use it When: You need to repair a Package on a specific DP (i.e. not all DPs).
• What it Does: Recopies the compressed version of the Package from the local Site Server to the DP. No files are copied from the Package source hence no WAN traffic is created (other than the instruction being sent to the Site Server to Refresh the Package).
  • Resets the Access Control List (ACL), if changes have been made to the Package Access Accounts.
  • Resets the Virtual Directory if BITS has been enabled or disabled on the DP since the last Package update.
  • Doesn't update the Package Source version.
  • Doesn't increments the Package version in Client Policy.