Not entirely the same idea, IMO.
- Fediverse is about software implementations and services being able to talk to each other.
- IndieWeb is about owning your online presence via your own domain name.
The core idea of the fediverse is that you have some software running on some domain, providing a service. The focus is less on having a website, and more on providing a way to talk to people on other services. Just like email is a service, and you can talk to people on other email services. Everything is a message. Messages are delivered over a special protocol in a special format.
The core idea of the IndieWeb is that you are identified by some URL. You are in control of a website or web presence specifically. You make posts to that website, and those posts live on a permalink. Other people can subscribe to feeds of your website and web posts. Everything is a web page. You add some extra markup to your HTML to provide identity, publishing, and subscribing endpoints.