At least in the US since the 60's, another way to divide conservatives has been in the party's three big issues: economic classical liberalism, social conservatism, and foreign-policy neo-conservatism. The moderate, short-term goals of these groups are sometimes in alignment, but their desired end-states look very different:

• Neo-conservatives want a big military and an aggressive foreign policy, whereas classical liberals hate war and want to shrink the military, along with the rest of the government; and religious conservatives (generally- the prevalence of the other groups has lead to abnormalities in the most famous preachers) hate war and love peace.

• Religious conservatives are generally fine with the welfare state and regulations, and support restrictive social laws; whereas classical liberals hate all of the above.

• Classical liberals want to shrink (or drown) the government, which both of the other groups oppose for various reasons: some to most religious conservatives like environmentalism and the idea of a safety net, and neoconservatives love the military.

There's also a distinction between traditional politicians who support negotiation, moderation, and compromise, and the Tea Party-backed groups who don't.