A distributed architecture generally refers to a single application or service designed to be resilient to individual data center failures. For example, Reddit, a centralized application controlled by Reddit itself, operates data centers around the world to process user transactions. In the event of an outage in a specific location, such as California, Reddit would still be able to function because its infrastructure for handling user requests and serving data would automatically switch to other functioning data centers elsewhere, like Nevada, Arizona, or Washington. This is an example of a distributed architecture.

On the other hand, a decentralized federation does not consist of a single application. Instead, it involves a software platform like Lemmy, which is hosted on multiple individual hosts. When a user signs up with one host, they can interact with users from other hosts, but each host manages its own infrastructure. For instance, someone could host a Lemmy instance on an old laptop they found in their closet and name it ballsuckers.com, while another person could host a Lemmy instance in the cloud with a properly designed distributed architecture and name it bingbong.com. Each host is responsible for managing its own instance. Users from both instances can interact with each other, but if, for example, the hard drive of ballsuckers.com were to fail, the entire ballsuckers.com instance would go down. However, this would not affect bingbong.com because its infrastructure is separate and managed independently.

I hope this helps!