Broadly speaking it seems mostly to be the point of focus. In Libertarianism it is all about the individual, having freedoms from others, and being an island.

In Anarchism it is about specific external coercive forces. Those forces impact individuals, groups, communities, and so on.

So a Libertarian may think about food security from a perspective of deregulating supply so that you can choose to buy unsafe food because you think it is a good idea. An Anarchist may instead think about mutual aid, local cooperative production, and preventing external power structures like corporations or governments restricting sharing of resources.