Azure AD B2B is only an Azure AD capability. It enables businesses to provide users from other tenants access to their applications and services. Nothing changes from the standpoint of your app. The Azure AD app is still the same. Azure AD B2B offers an API that can be used to develop flows for inviting users from other directories, but it won't change the look and feel of your app.
Azure AD B2C is a service based on the same technology as Azure AD but with different features. The goal of Azure AD B2C is to provide a directory for consumer apps, known as Federation Gateway, where customers may register using their e-mail ID or social services like Google, Facebook, and MSA. The purpose of Azure Active Directory B2C is to allow organizations to manage single directory of customer identities shared among all applications i.e. single sign-on.