Distinction between Dharmaguptaka and Mahayana

what's the distinction between Dharmaguptaka and Mahayana? I know that the former is an ordination lineage with specific vinaya as distinct from Theravada ordination, but I don't understand where Mahayana may encompass Dharmaguptaka, or where Dharmaguptaka may encompass Mahayana, or neither. I would be interested in a Venn-diagram type of answer, and similarly for the same question asked of Mulasarvastivada and Vajrayana. In the same way, is Theravada both an ordination lineage and a sect? Is the question valid?