Question: What tax deduction classification do you give to name the difference between the amount billed and the amount paid by an insurance company?
Answer: It depends upon whether you are contracting with the payer or not. If you are contracting the difference between the office fee (amount billed) and the amount paid by the payer + the patient's co-pay or coinsurance is known as the contractual obligation (aka: write-off, allowance or adjustment).
You cannot claim it as a tax deduction since you signed an agreement stating that you agree to accept the payer fee schedule as payment in full. If you are not contracting with the payer you can balance bill the patient for the difference.