Google uses Consoles as a way to view sets of related services.
Fundamentally, Google projects (which are the groupings of services, credentials etc.) behind these views are what's being presented and these (projects) are the same regardless of the console being used.
So the following show 2 ways to view the same project:
PROJECT=[[SOME-GOOGLE-PROJECT]]
https://console.developers.google.com/?project=${PROJECT}
https://console.cloud.google.com/?project=${PROJECT}
Developer Console (or was it API Console? used to be?) the default view into Google Cloud Platform projects but the modern way to do this is via Cloud Console.
There is also a Firebase console, Home (Actions) console, Apps Script console etc.
Sometimes Projects are only available under the console they were created under, but fundamentally, there's only one type of Google Project.
Aside: One aspect of all Google projects is that they contain the Google APIs (or services) that have been enabled for the project. One very powerful feature of Google is that every public Google service is 'shaped' similarly:
https://developers.google.com/apis-explorer
All Google services are accessible via REST, described by a so-called discovery document (which are exposed by a meta-service called the Discovery Service), use auth consistently and have so-called API Client Libraries published in several languages.
Google is moving to a model in which its services are also exposed (as they are internally) using gRPC. During this transition only some of its services (primarily Cloud) are available over gRPC too.
Suffice to say that, while Google often presents itself as a distinct set of technologies, these technologies are, in fact, remarkably consistent.