In the 18th & 19th centuries, rubato meant more than generalized freedom
in the playing.  Mozart bragged that his left hand (playing rhythmic
figures) stayed in strict time while his right took liberties but caught
up eventually with the strict accompaniment.  "I am always strictly in
time. They all wonder at that. They cannot understand how I keep the
left hand independent in the tempo rubato of an adagio, for with them
the left hand always follows the right."

In the liner note for a Horszowski recording of the Mozart sonatas, Allen
Evans writes, "While it seems paradoxical to play one hand evenly while
giving full liberty to the other, Sir Charles Halle recalled Chopin's
similar rhythmic treatment as being so subtle that it took him years to
realize how Chopin altered beats in his Mazurkas."

In the early 20th century, the Polish pianist Paderewski argued against
the notion of "catching up" by the end of each bar or phrase.  He argued,
"We duly acknowledge the highly moral motives of this theory, but we
humbly confess that our ethics do not reach such a high level. The making
up of what has been lost is natural in the case of playing with orchestra,
where, for the security of the whole, in spite of the fractional alterations
of the movement, the metric integrity should be rigorously preserved.
With soloists it is quite different. The value of notes diminished in
one period through accelerando, cannot always be restored in another by
ritardando." His thesis apparently was so persuasive that <The Grove
Dictionary of Music and Musicians>, the bible of music reference books,
altered its definition of the term in its next edition.  See more on
this at

  http://www.usc.edu/dept/polish_music/PMJ/issue/4.1.01/paderewskirubato.html

In my experience, ad libitum has never been encumbered with such debate.
The term literally means "at liberty" or "as you please," and how much
freedom (within the bounds of good taste) is left to be decided by the
interpreter.  A typical online definition of the term: "<Ad libitum>
also written as 'Ad lib' means 'at pleasure' or 'leisurely.'  It often
signifies that the passage following it should not be played in a strict
time, but rather freely. This is often used in solos, especially in jazz
improvisation."  (The Open Encyclopedia Project, www.open-site.org)

Nick Jones
Atlanta
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