Is Pulumi "under the hood" terraform to deploy infrastructure ?

no. We use some terraform providers to define the schema for our SDKs (which we call "bridging" a provider), but the provisioning logic, engine and CLI don't use terraform in any way

Ok nice.

also, only some of the providers are terraform. the kubernetes provider, e.g., is built from scratch, and it’s vastly better.

'vastly better', nailed it

😁