A civilization is a culture of a certain scale and complexity. All civilizations are cultures, but only a small subset of cultures are civilizations.
As the Wikipedia article on civilization puts it:
Historically, a civilization was a so-called "advanced" culture in
contrast to more supposedly primitive cultures... In this
broad sense, a civilization contrasts with non-centralized tribal
societies, including the cultures of nomadic pastoralists, egalitarian
horticultural subsistence neolithic societies or hunter-gatherers... Civilizations are organized in densely populated
settlements divided into hierarchical social classes with a ruling
elite and subordinate urban and rural populations, which engage in
intensive agriculture, mining, small-scale manufacture and trade.
All human populations participate in one or more cultural groups regardless of whether they are part of a civilization.