Can I have deductible, copay, and coinsurance on the same claim?

Sometimes, depending on the service and your plan design. The EOB usually shows how the insurer applied each part.

Which one usually causes the biggest surprise bill?

Deductible and coinsurance often create the biggest surprise because they can lead to larger balances than a fixed copay.

Deductible vs Copay vs Coinsurance

A deductible is the amount you must pay before your plan begins paying for many services. A copay is a fixed amount for certain services. Coinsurance is your percentage share of covered costs after deductible rules apply. These three terms often explain why you still owe money after insurance.