Answer
Is a responsive website the same as a PWA?
No, they solve different problems. Responsive design means your layout adapts to different screen sizes using CSS (media queries, flexible grids). A PWA is about adding installability, offline support and push notifications through HTTPS, a Web App Manifest and a service worker. A site can be responsive without being a PWA, and in principle a PWA could be built without fully responsive layout, though in practice almost every PWA is also responsive.
Responsive design
Purely a CSS/layout concern — media queries, flexible units, images that scale — with no relationship to service workers or manifests.
PWA requirements
HTTPS, a manifest and a service worker are what unlock installability and offline behaviour, regardless of whether the layout is responsive.
Why they are usually combined
Because PWAs are commonly installed on phones, tablets and desktops, responsive layout is a practical necessity for a good PWA experience, even though it is not a technical requirement.