The neo prefix in those words are there for different reasons. Neoliberalism is new (neo) because it it's a new kind of liberalism that came to be after Keynseianism replaced liberalism for a few decades; it's the ideology that's new. The newness of neoconservatism refers not exactly to the ideology, but to the people to whom it belonged; the original neocons were often former leftists, usually of Trotskyite varieties, who were becoming conservative hawks; i.e., they were new to conservatism. Most current neocons aren't former trots anymore, in fact, most neocons haven't been former trots since the 70s and 80s, which was before the foreign policy ideology really became institutionalized big time (peaking with the Bush II Administration, but the Reagan and especially Bush I Administrations were trial runs and the Obama/Trump administrations continued it and Biden appears to be as well) but the name stuck.
The neo prefix in those words are there for different reasons. Neoliberalism is new (neo) because it it's a new kind of liberalism that came to be after Keynseianism replaced liberalism for a few decades; it's the ideology that's new. The newness of neoconservatism refers not exactly to the ideology, but to the people to whom it belonged; the original neocons were often former leftists, usually of Trotskyite varieties, who were becoming conservative hawks; i.e., they were new to conservatism. Most current neocons aren't former trots anymore, in fact, most neocons haven't been former trots since the 70s and 80s, which was before the foreign policy ideology really became institutionalized big time (peaking with the Bush II Administration, but the Reagan and especially Bush I Administrations were trial runs and the Obama/Trump administrations continued it and Biden appears to be as well) but the name stuck.
Names are stupid.