I wonder if you're confusing libertarianism with liberalism.
Liberalism is the standard definition of what you're used to, implying freedom, tolerance, and most importantly state welfare.
Libertarianism on the other hand is an extreme variation of liberalism that advocates a minimalist state that does not even intervene to protect the rights of citizens from each other. It is essentially a 'survival of the fittest', no restrictions type of society. The state's only role would be to defend the nation from other countries. There would be hardly any taxation, and absolutely no welfare.