Not exactly. Yes, I would probably characterize Firebase as a PaaS, but Google Cloud is much more than just IaaS, as it includes some PaaS components, like App Engine.
I would say the general idea behind Firebase is that it is designed to build fully functional applications without any additional components. E.g. you could serve your static web app using Firebase Hosting, manage users with Firebase Auth, use Firestore for data storage (the syncing features of Firestore are truly amazing if you're not familiar with them), and tie things together with Cloud Functions. Also, note that while Firebase was originally pretty heavily focused on mobile, especially native mobile, most of their services work great on the web regardless.
The other thing about Firebase (referencing the previous comment about it being a little weird as a "Cloud in a Cloud"), is that it essentially exists on top of GCP. For example, a Firebase Project is really a GCP project under the covers, Cloud Functions for Firebase are really some syntactic sugar on top of GCP functions, etc. While that can be a little confusing at first, it can provide some great value. We have apps where most of our backend is in GCP (e.g. running Node in App Engine Flexible, using Cloud SQL Postgres for our DB, using Cloud PubSub topics for our eventing system, etc.) but then we use Firebase Auth for our user authentication, Firebase Hosting to serve our React app, etc.
Yes, I'm a definite Firebase fan boy, but that's because I feel like I can be so productive with it, without needing to worry much about underlying infrastructure, while still being easy to integrate with the horsepower of GCP.
