Staff augmentation and contract staffing are frequently sold as the same thing, and the difference matters. In augmentation the person joins your team, takes direction from your leads, works to your backlog and is subject to your engineering practice. You own delivery. We own supplying and supporting the right capability.
That boundary sounds obvious and is routinely blurred in practice, usually in one of two directions — either the supplier is held accountable for delivery outcomes they cannot influence, or the augmented person is excluded from the team's decisions and context while still being expected to produce as a full member of it.