I guess it depends on what you mean by "under the hood". As far as I know it doesn't use Terraform during runtime but it uses the Terraform resources for generating language definitions. It has a lot of interoperability tools as well such as a "terraform bridge" and a tool that converts Terraform projects.
xyzzy123 already described the differences between Pulumi and terraform, but I want to add one key way in which they are similar:
Pulumi uses terraform under the hood. We get all of the reliability of terraform, but with a much more powerful runtime engine.