Service Bridge is the application that connects two ServiceNow instances to each other for the use case where one instance is a "producer", i.e. a provider of services, and the other is a "consumer", i.e. a customer of the producer instance that requests services and receives certain data syncs.
Service Bridge only connects two ServiceNow instances, it cannot be used to connect third-party applications.
Service Builder is a graphical user interface that helps you build out service-layer configuration items in a user-friendly way. It's not an integration tool. Docs - here
