The phase qubit is closely related, yet distinct from, the flux qubit and the charge qubit, which are also quantum bits implemented by superconducting devices. The major distinction among the three is the ratio of Josephson energy vs charging energy[3] (the necessary energy for one Cooper pair to charge the total capacitance in the circuit):
For phase qubit, this ratio is on the order of 106, which allows for macroscopic bias current through the junction;
For flux qubit it's on the order of 10, which allows for mesoscopic supercurrents (typically ~300 nA[4]);
For charge qubit it's less than 1, and therefore only a few Cooper pairs can tunnel through and charge the Cooper-pair box. However, transmon can have a very low charging energy due to the huge shunt capacitance, and therefore have this ratio on the order of 10~100.[5]
^Barone, Antonio; Paternò, Gianfranco (1981). Physics and Applications of the Josephson Effect. New York: Wiley.
^Nielsen, Michael; Chuang, Isaac (2000). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.