I'm not sure, I understand neoliberalism as a set of beliefs specifically about how the economy should be run, and libertarianism as a philosophical position an

I'm not sure, I understand neoliberalism as a set of beliefs specifically about how the economy should be run, and libertarianism as a philosophical position and system of morality. So my understanding of the relationship between the two is that libertarians tend to hold neoliberal beliefs about the economy, and many neoliberals are libertarians. But it's perfectly possible to hold neoliberal beliefs and not be libertarian (for instance, you could be a religious fundamentalist who believes the state should be run as an autocratic theocracy, but who also believes the economy should be run according to free-market capitalist principles). If that's correct, my usage of neoliberal seems alright to me.