The AWS official site reads role as a collection of permissions and group as a collection of users. But still they look the same to me. You attach policies to groups or role
AWS Groups are the standard groups which you can consider as collection of several users and a user can belong to multiple groups.
AWS IAM Roles are all together different species; they operate like individual users except that they work mostly towards the impersonation style and perform communication with AWS API calls without specifying the credentials.
Given that IAM Roles are little different, I am emphasizing only that. There are several types of IAM Roles like EC2 IAM Roles, Lambda etc. If you consider, you can launch an EC2 instance with an EC2 IAM Role; hence forth any AWS API related communication wouldn't require any AWS Access Key or Secret key for authentication rather can call the APIs directly (however the long answer is - it uses STS and continuously recycles the credentials behind the scenes); the privileges or permissions of what it can do is determined by the IAM Policies attached to the IAM Role.
Lambda IAM Role works exactly the same, except that only Lambda function can use the Lambda IAM Role etc.