Both types of group projects look at the direct paternal lineage. However, they have different starting points.
A Y-chromosome DNA (Y-DNA) haplogroup project starts from the founding of a particular haplogroup or subclade. It traces that lineage forward.
On the other hand, a surname group project starts with men who share a surname (or variant). The surname project traces men back to a common ancestor.
In many ways, the two types of project support and augment each other.