Many people confuse copayments with coinsurance, but they are two completely different terms where your health insurance is concerned. Copayments are the amount you must pay out of pocket for each doctor visit, and coinsurance is the portion of the medical bill you must pay, up to the cap specified in your policy. It is not unusual to have both a copay and coinsurance costs.
As an example of how copays work, if you visit your regular doctor, your copay is one amount, but if you are referred to a specialist, that copay is a different amount completely, based in part on the type of procedure you are having performed. The copay will always be the same for the same procedure for each patient. That is basically the way a copayment works.
Coinsurance is the percentage of the policy you are agreeing to pay out of pocket, up to a cap, or specified coinsurance limit. For example, if you have 20/80 coinsurance with a cap of $2000, you must pay 20% of all medical costs until you have paid in the amount equal to the cap. So for every $100 of medical costs, you would be responsible for paying $20, until the total amount you paid was equal to two grand. Once you reach the cap, the medical insurance will pay 100% of future medical costs.
One way to lower your health insurance premium is to elect a higher coinsurance ratio. If your ratio is 50/50, it will cost you more out of pocket until the cap is reached, but your premiums would be much lower. And since you are paying a higher amount of the costs out of pocket, the cap would be reached sooner than with a lower ratio. This method will only work if you are financially stable enough to afford potentially high coinsurance payments for a while, but it works out as a way to save a great deal of money on premiums in the long term.