Obviously, you aren’t comprehending the distinction. A “Big L” Libertarian is a member of the Libertarian Party and runs for office as a Libertarian. A libertarian Republican holds libertarian ideals but is a Republican. There are classical conservatives, moderates, “neo”-conservatives (though that term gets misused a lot) and libertarian Republicans.
Based on what I’ve heard from Ron Paul, he is libertarian at the federal level, but more of a classical conservative at the state level. There’s nothing wrong with that. Even though I don’t agree with him on everything, there are many, many issues on the federal level that I like. He is a original intent Constitutionalist. Most Republicans lean that way.