You can also add Scott Walker to that list and Chris Christie is very likely to run as well. Also some fringe guys like Ben Carson and Donald Trump but they don't really count. I'll focus on the differences because they'll all have a basically conservative platform on most issues.

Scott Walker and Jeb Bush are way out in front of everyone else at the moment. They're considered the most 'mainstream' candidates and people consider them to be the most electable in a general election (think Romney). Walker is defined by his budgetary work in Wisconsin and people will argue for and against that record. Bush is defined by straying from the GOP platform on both Common Core and immigration reform.

Ted Cruz is the religious right's pick (think Santorum) and is defined by his strong stances against the current Obama administration. Should he make it out of the primary he would be painted as the poster child for the Republicans being the 'Party of No'.

Marco Rubio is a young senator who's been on the fast track to the presidency (think Obama) since he made it to the senate. He's defined by his foreign policy record, which he's made a point to hone ever since he got into office. He's seen as a long shot because of his youth and inexperience and will most likely of anyone to wind up on a ticket as vice president.

Chris Christie is thought of as a pragmatic and competent politician but also somewhat of a bully (think Rahm Emmanuel). He's seen as being a career politician rather than standing for conservative principles.

Rand Paul is the GOP's real wildcard. His father was a Republican in name but a Libertarian in principle and for a long time was the most influential Libertarian politician in the country. Rand isn't as much of a Libertarian as his father but his primary issue is a non-interventionist foreign policy, which resonates strongly with American voters but NOT with the GOP base.