It's not that it's more expensive at one place or another for the most part. When you go in-network you are seeing providers that your insurance has a contract with. This contract includes agreed amounts for procedures. Providers will often grossly overbill (mostly because it's easier to let the billing backend resolve these limits than bill accurately in the first place) and your insurance will respond with the amount covered. The remaining amount of the bill is written off because it was in-network so the provider is not allowed (by the contract with your insurance) to bill the balance not covered to the patient.

Out-of-network does not have this protection. Your insurance will possibly cover some of the bill, normally up to some percentage of what they consider a normal amount for the procedure in the area, and then you will be billed for the entire balance. Say your provider bills $100k and your insurance says they think that procedure normally only costs $50k and you have 80% out of network coverage. You would be billed for 20% of the $50k covered as coinsurance, plus the remaining $50k that would've been written off if you were in-network.

This is generally how people get surprise bills.

For a real world example: last year my insurance got billed ~$3k for a routine blood test for my wife as part of an annual checkup. It was in-network and the insurance paid $27 and the provider wrote off the rest.