Hashtags are passive filters for your server's federated timeline. They will show posts from other servers, but only if your server has noticed the post anyway (there's a list here of what servers notice: https://fedi.tips/which-posts-and-accounts-can-i-see-from-my-server/).
Groups work totally differently, they actively push all their content to everyone who follows the group, even if their server hasn't noticed that content yet.
So, Groups federate much more effectively.