Definition #1 applies to Libertarians. They want to restore the traditional idea of limited government in all forms as it use to be. Get back to that form of government and resist changing it. Definition #2 defines "Neoconservatives" who are significantly different from true Conservatives.
Allowing people social freedom is a true Conservative idea as it falls under limited government. Taking away individual rights is a Neoconservative idea.
Definition #2, as originally state, is a common (incorrect) definition of conservative. Neo-conservative just describes a sub-set of conservatives who believe in a different kind of foreign policy.
Conservatives have long believed in limiting individual rights. Prostitution, pornography, sodomy, polygamy, homosexuality, gambling, legalization of drugs, censorship of speech and press, abortion, etc., all usually on moral grounds or in the interests of nationalism. So, by laying claim to conservatism as a libertarian, you rightly claim economic conservatism, but also wrongly claim social conservatism. That's where the problem lies.
Regardless,
liberal is the more correct label.
Definition according to Merriam-Webster:
lib·er·al - adjective
1. favorable to progress or reform, as in political or religious affairs.
2. (often initial capital letter) noting or pertaining to a political party advocating measures of progressive political reform.
3. of, pertaining to, based on, or advocating liberalism.
4. favorable to or in accord with concepts of maximum individual freedom possible, esp. as guaranteed by law and secured by governmental protection of civil liberties.
5. favoring or permitting freedom of action, esp. with respect to matters of personal belief or expression: a liberal policy toward dissident artists and writers.
6. of or pertaining to representational forms of government rather than aristocracies and monarchies.
7. free from prejudice or bigotry; tolerant: a liberal attitude toward foreigners.
8. open-minded or tolerant, esp. free of or not bound by traditional or conventional ideas, values, etc.
That is, of course, if you follow dictionary definitions. If you follow Definition #2, which is not in the dictionary but how the word liberal is most commonly applied by most people, liberals are socialists.
