It seems context determines whether they do. Live large is an idiom (here) which means "to live in luxury; to spend time in grand style", as in George loved to live large, dining at fine French restaurants.
Neither live big nor live high seems to be set phrases, in which case their meanings have to be interpreted ad hoc. As for live big - appearing in the title of the book by Katie Brazelton: Live Big! 10 life coaching tips for living large passionate dreams (2009) - I'd say it doesn't mean the same thing as live large above. It's closer to 'to live in hope' or 'to live one's dreams'. Here's from the preface:
"Before we dive in to talk about huge hopes and daring dreams, I want to pause for a moment and make sure that we actually have our eyes set on our only real hope for the future. That can be none other than God, the One who holds our future in His hands."
Regarding the meaning of live high in the song Live High by Jason Mraz, who according Wikipedia "lives a health-conscious lifestyle and enjoys eating mostly raw vegan foods," it seems to me it has moral connotations. The lyrics goes: Live high, Live mighty, Live righteously, Takin it easy. In other words: Set your morals high and live them.