The short answer to your title question is yes.
The game originally released for the PlayStation 1 (Final Fantasy Tactics) is indeed different from the one you purchased on your iPhone (Final Fantasy Tactics: The War of the Lions).
To quote directly from Wikipedia's section on Versions and re-releases:
A PlayStation Portable version of Final Fantasy Tactics, entitled
Final Fantasy Tactics: The War of the Lions was released on May 10,
2007, in Japan; and is now released across all regions. It is the
second game announced as part of the Ivalice Alliance. The game
features an updated version of Final Fantasy Tactics, along with new
features including in-game cutscenes, new characters, and multiplayer
capability. The updated mechanics contain a 16:9 widescreen support,
new items, new jobs, and cel-shaded full motion videos. The English
version contains full voice acting during the cinematic cut scenes,
whereas the Japanese version does not.
War of the Lions was ported to
iOS in 2011, with the iPhone version released on August 4, 2011, and
an iPad version was released February 2012.
There are many websites offering job trees, but I found that this one was particularly well-suited for my iPhone screen: FFT Job Tree