Unfortunately there are many more, and not just the two that the simplistic libertarians claim.
What about the "this needs to be in the constitution" vs. "this needs to be handled by the states" axis? Some conservatives favor a stronger DOMA that would make gay marriage illegal throughout the country. Others want this handled on a state-by-state basis. Similar arguments go both ways on abortion, environmental regulations, business restrictions, etc.
The debates on if/when to use the military are often argued out on a "realist" vs. "idealist" axis.
Even if you stick to conservative vs. liberal, there are differing opinions within the conservative ranks regarding such things as Social Security. There are conservatives who feel that promises were made and need to be kept. Others who think those promises should never have been made and the program should be scrapped post-haste. Others believe it just needs to be "privatized", but every privatization scheme I've seen has had a large government component to it. What is the "real" conservative position on Social Security? Medicare? Private pensions (where promises were made and contracts signed for good or ill)?
“”...there are differing opinions within the conservative ranks regarding such things as Social Security.”
Does Part 2 apply the F test?