What's the difference between tp and teleport?

Update:

As mentionned by ppperry in the comments, this answer is no longer valid I'm afraid.

Tp is now a simple alias of Teleport /tp is now an alias of /teleport (much like /w, /msg and /tell). /teleport has been simplified a bit, to avoid ambiguity. Source

Old Answer:

• When running a /tp command and using relative coordinates, the coordinates are calculated from the entity focused by the command
  • When running a /teleport command, relatives coordinates are calculated from the entity who is executing the command

Source with exemple and screenshots (in french) : fr-minecraft.net/news-minecraft-1820

exemples :

/execute @e[name=Zomb2] ~ ~ ~ tp @e[name=Zomb1] ~ ~3 ~

will teleport the zombie "Zomb1" 3 blocks above the position of "Zomb2" (as it was Zomb2 that executed the command)

 /teleport @e[name=Zomb1] ~ ~3 ~

will teleport the zombie "Zomb1" 3 blocks above you