But libertarianism isn’t a philosophy, is it?
Everyone has at least an implicit philosophy. For Libertarians, the denial of the need for a philosophical base for politics is a part of their implicit philosophy.
So in the field of politics, libertarians draw the same conclusions as objectivists because the libertarian principle (liberty) implies everything an objectivist can expect from a government
Not quite. Libertarians at best tend to dodge the issue of what exactly they expect from a government; at worst, they are explicit anarchists.
If you ask them, “Is it OK for the government to violate the rights of individuals?” they will say exactly what Objectivism says: “No.” But if you ask them, “Should the government make laws against crime? Should the government prosecute and punish criminals? Should the government maintain a standing army and use it actively against foreign threats?” they will either hem and haw and refuse to give a clear answer–or give a clear answer of “No.” Objectivism, by contrast, answers all those questions with a definite, uncompromising “Yes.”
So the similarities go only as far as the negative–what the government shouldn’t do–but they are absent when looking at the positive, at what the government should do.
so it differs in private issues, right?
Yes, it differs very much in private issues.