In aws how to access service in a different region from a VPC

Consider the following situation in AWS:

1. A VPC in region A with many servers.
2. A mysql service in a server with public IP in region B. This service's port(3306) is open to (0.0.0.0).

from any server in VPC that has public IP I can access the mysql server in region B but any server that doesn't have public IP is unable to access the server.

what is the reason for this? is it possible the servers without public IP access has different way of communicating in different way?

just as a NOTE:

the services without public IP seem to show the NAT's IP:

curl http://icanhazip.com result is: NAT's public IP