D-Wave works more like a quantum simulator. It has a grid of two-level quantum system 'qubits'. However any single qubit cannot be arbitrarily rotated like in a universal QC.
All qubits form a collective state that is the ground state of some Hamiltonian. The Hamiltonian is parametrized by a set of coefficients. Initially the coefficients are set so that the ground state is something simple and it is implemented in the state of the qubits.
The As the 'quantum computation' proceeds, the Hamiltonian coefficients are slowly changed and the ground states becomes something more complicated. If the change is slow enough the initial ground state should become the final ground state - the object of interest.
The qubits are still the same thing - two level quantum systems, however, the way in which they can be manipulated is very different from the one in a universal QC.
There are works that show that the D-Wave model of computations is equivalent to the circuit one, but this requires a lot of qubits.