Well, Connections does not supported tags. It is a feature in WordPress most people do not even use so I have not been in a hurry to add support for them. If they feature were added, the tags would be unique to Connections too. Just like the categories are.
That said… Connections does have a rather unique feature that I added a long time again… it should still work perfectly. It is the wp_current_category shortcode option. This sounds like it might be something that would work for your needs.
Does that help?