I'll start with the German system. Here you are either automatically insured in one of the public insurances (there are many), which marginally differ in their cost (think single digit euro differences) and have to cover basically the same procedures. If one reaches a certain income level, being privately insured is possible.

If you are publicly insured, you wont see most costs, as these are directly handled between your insurer and the doctor/hospital. For some medications and procedures there are co-pays that are flat fees (5 Eur for Medications, ...).

Access to specialists mostly need a referral from your family doctor.

In private insurance, often you yourself will be billed and you will need to hand this to your insurance company.

The good side is that in most common situations I have never needed to worry about cost in public insurance, wait times for referrals can be very long and understanding what you need to get certain care can be very difficult. Private insurance often has better payment schemes for providers and less artificial limits on number of patients or which doctor is able to provide services, so access to most care is faster and more widely available.