A Internet gateway is a horizontaly scaled, redundant and highly available vpc component that serves as a bridge between your private virtual network and the outside cloud. It provides a target for your vpc route tables for Internet-bound traffic and performs network address translation (NAT) for instances that have been assigned public ip addresses.
Transit gateway acts as a central clouds router, creating a simple hub and spoke network to connect multiple isolated networks like cloud environments, data centers and remote offices. Instead of creating complex, direct connections between every single network, everything connects just once to the central gateway.
You need to use transit gateway peering connections to connect vpc's across different AWS Regions. This creates a direct, encrypted and private connection that travel over the global network rather than public Internet.
A vpc peering connection is a direct, private networking link between two vpc's. It allows resources like EC2 instances to communicates using private IP addresses as if they were in the same network. The traffic never traverses the public Internet, ensuring high security and low latency .
Setting up and running an amazon vpc peering connection is free. You pay only for the data transferred over the connection. And even then, traffic that stays within same AZ is entirely free.