Hmmm. I believe single payer is when the government covers all basic costs, so single payer is a sub-set of universal health care. Universal health care just means everyone is covered one way or another. Could be by government programs or private insurance.
For example, in Canada basic health care (doctors and hospital care) is covered by the government, so that's single payer universal health care.
Dx'ed in 1999. No surgeries.
Current meds: 75 mg 6MP. 20mg prednisone.