No, you can opt out or opt in for notifications on a post by post basis as ShaneJ mentioned above. Notifications mean you will get an email. That email can be configured to be just a notification that an update has been made, or can actually contain the content of the update. Notifications have no correlation with "show recent replies to your posts".
I assume you are not getting an email notification when someone posts to the "Beekeeping Test" topic? This means you are not subscribed for notifications. But if you have made a post on that topic, it will still show up in "show recent replies to your posts".
Not to make things more confusing, but if you do subscribe to a given topic for notification, it will only send you one notification until you visit the topic, which will reset the notification. In other words, if you look at the thread before going to work, and 15 people comment on the post while you are at work, only the first comment will cause an email notification to you.
Hope this helps