Imperialism is the highest stage of capitalism, defined by the dominance of finance capital (over industrial capital) and its export from the imperial core to the periphery.

Neo-colonialism is a specific case of a relationship between an imperial core country and a periphery country, where the periphery country is nominally independent, and the imperial core country uses indirect means of intimidation (instead of direct colonial rule). I would also note that the terms neo-colonialism and colonialism center the colony/periphery, while imperialism centers the imperialist state. So it is still the same phenomenon, the terms just focus on different parts of the relationship.