Common buckthorn and Euopean buckthorn are the same species. if the cambium is bright orange, its a buckthorn.
I've cut buckthorn where the heartwood was not orange, but peachey/salmony, so an orange heartwood is not a good indicator. Leaves and fruit are the best indicators for plant ID. Don't know why you think the berries should be red on buckthorn, they are black when ripe.