Network transfer costs though NAT GW

Customer has a question on how costs are allocated for outbound traffic through a NAT GW.

What they expect & what support has shared with them is that any traffic going out to the internet (to a public IP) will count as "Data transfer to the internet". But looking at cost explorer what they are seeing is an EC2 to EC2 transfer cost. They are indeed sending traffic to a public IP on an EC2 instance in another account but since they are using the public IP they expected to see a data transfer out to the internet charge.

They are trying to accurately forecast costs for a service they are building so would like to know how these two are distinguished so they can forecast correctly. Will they always see an EC2 to EC2 charge for outgoing NAT GW traffic if its going to the public IP of an EC2 instance?

Thanks!