Are these 2 totally different things or are they roughly same/similar in what they can accomplish?
Azure Worker Role is your own set of virtual machine in a "application farm". You can run any code on them in a distributed fashion. Typically, you write business code to run on these servers (ie: order processors, customer emailers, cloud-to-premise synchronizers, etc)
Azure Automation is meant more for automating administrative tasks such as:
Azure Automation is written in Powershell which is great for accomplishing small administrative tasks. I would not want to write a complex order processing system in Powershell though :O
Furthermore, with Worker Roles you kind-of have decent control over the VMs that run your code. Can install third-party components on them, access local storage, basically do whatever a regular C#/VB.NET program can do. Automation is a service to automate admin tasks.
HTH