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Not knowing terminology is not a problem,except to that it makes it harder to get ideas across.
I now understand what you are talking about. I think of them as "connections". This is a handy feature, it just requires a couple of specific conditions to work. Conditions which are easy to miss.
First Condition:
The only way I know of for connections to work is inside of the "Drawing Canvas". That applies in 2013 and back to 2003 (actually 2002) also. If I create shapes outside of the drawing canvas, the connection lines won't "stick".
In 2003 you turn on automatic creation of the canvas in Tools menu > Options command > General tab > "Automatically Create drawing Canvas when inserting autoshapes"
In 2013 you do File menu > Options command > Advanced option > Editing options section > "Automatically Create drawing Canvas when inserting autoshapes"
Second Condition:
You have to use specific "connection lines", not just any lines. In 2003 it was easier to identify them because you when you clicked on the "autoshpes" command (in the drawing toolbar) there was a "connections" category". I don't see that category any more in the ribbon versions. Instead, in ghe shapes gallery when you hover over a line you have to wait to see the title and pick a line that includes "Connection" in the name. You can visually tell the difference between the 2 types of lines by looking , very carefully, at the little "handles" at the ends of the lines. Regular lines have clear circle handles. "Connection" lines have green filled circle handles. When you drag a connection handle over a shape, the connection points are highlighted as tiny circles that are easy to miss.