When you create a connection type by dragging a connection from one element type to another in the Planner, you create both the connection type and the connection instance. Connection types are all instances of a connection and connection instances are specific element types that are allowed to use that connection.
For example you might have "Thing" and "Other Thing" in your cognitive city. If you drag a connection between the two and give it a name, say "has" you have both created the connection type "has" and the allowed instance "Thing has Other Thing". You can then use that connection type between more element types, creating additional instances.
If you click on any connection in the Planner you will see its with all of its instances in the right hand panel. When doing deletions you need to be careful about what you are deleting. If you wish to delete only a specific instance of the connection (and all connections of that instance) you should do it with the "x" next to the connection instance in the panel (the "x" will not appear until you hover over it). If you use the options at the top and select "Delete" it deletes every instance of connection of that connection type.
For example, the screen shot below shows how to delete every "has" connection vs how to only delete the "Thing has Other Thing" connections.