neoliberalism is notionally centered on things like free markets, globalization, free-trade, privatization, deregulation, etc. and can be seen as a sort of pro-business or pro-corporate philosophy.
i'd say 'conservative' is really a question of preferring the status-quo, or perhaps traditionalism. consider that 'conservative' can imply potentially very different views if you contrast US and EU conservatives (or elsewhere). a conservative is better contrasted with a 'progressive' who enthusiastically seeks (perceived) beneficial changes to the status-quo or traditions.
“pro-corporate”, perhaps, but corporatism is a different thing and opposed to neoliberalism. (It doesn't come from “corporation” in the sense of the business enterprise, but from the same root referring to a body, in this case referring to the whole of society as a single body.)
While neoliberalism and libertarianism are in the same direction, they aren't the same thing. Neoliberals are generally fine with government restricting what can be bought and sold, they just want most legal goods and services to generally be provided by private enterprise with limited regulation, and with only very limited barriers to international trade in goods and services that are legal in both the source and destination jurisdiction.
Neo-Liberalism is the ideology of the discovery of law through economics (which is held to be a sort of axiomatic "scientific" given). Basically if corporations were people -- and hey look here, they are -- and were to get together and dream up an ideology for themselves -- you know, corporations of the world, unite!! -- they would task some of their human lackies to manipulate their institutions to install Neo-Liberalism as the world wide political-economical regime.
Any other questions?