The terms for Apprentice and Padawan are interchangeable.
In Episode 2, Master Kenobi often refers to Anakin as 'my very young apprentice' when he's chiding him for a decision he's made. He also uses the term 'padawan' for Anakin at a couple of points.
See article here: http://starwars.wikia.com/wiki/Padawan
A Padawan, Padawan learner, Jedi Apprentice in Basic, or Jedi in Training, referred to a Force-sensitive adolescent who had begun one-on-one instruction with a Jedi Knight or Master outside of the Jedi academy. Having passed the Initiate Trials and ascended in rank from an Initiate, Padawans were given more responsibilities within the Jedi Order but were subject to the demands of their masters.
We can also see the definition for padawan here, from:http://www.definitions.net/definition/padawan
Origin: Coined by George Lucas for the Star Wars franchise. Sometimes said to have been derived from Sanskrit, or from Padawan, a region of Malaysia.
From what I saw during research for this, there is no in-universe explanation for the origins of the term. Before episodes 1,2, and 3 Apprentice was just used to describe a Jedi learner, but in the newer episodes the terms are interchangeable. Lucas didn't really make a backstory for why this is the term in-universe from the looks of things.