What's the difference between a libertarian and an anarchist?
They both seek freedom from social responsibility.
They're both, in practical terms, non-participants in the political process.
Politics is not a process.
Libertarians tend to desire a minimalist government. They support the Constitution of the United States and the constitutions of the various States, but want to see government limit itself solely to the authorizations and powers listed in these documents.
Which is what it should be anyway.
Of course, people have lived so long with the federal government agencies and programs that are far beyond the Constitution, and have even become dependent on it, so moving back to Constitutional government is going to be too big a change all at once.
Republicans also desire to see Constitutional government, but realize it's going to take a while to get back to it. That's really the biggest difference between what you call the 'tea party' and the Libertarians. They have the same ultimate goal, but the Libertarians tend to be impatient about it.
An anarchist wants no government at all. No constitution, no States, no federal government, no nothing...not even a government by popular vote (democracy). Such a scenario would mean no police, no army, no government taxes, no anything. It is, essentially, lawlessness.
A recent example of anarchy was CHAZ in Seattle (at least initially). It then tried to evolve into a democracy. in a short time, one faction became stronger than the others and it started to become an oligarchy. The breakdown between factions in CHAZ resulted in several shootings, and the destruction of CHAZ from within.
Similar patterns can be seen in other CHAZ attempts (currently in Portland, OR and in Minneapolis).