I think I know what you are having trouble with.
There are two different linkages in glycogen... there is the chain link and the branching link.
The chain link is from the O on carbon 4 to the anomeric carbon to the left of it
The branch link is from the O on carbon 6 to the anomeric carbon to the left of it
The "extra" carbon is always there... there are just two different links happening in glycogen that are similar enough that they look the same, but then upon looking further there seems to be an extra carbon. Look a tad bit further and you'll realize that it's on a different part of the glucose all together for those branch links.
NOTE, the squared bends in the non branch links of top picture are NOT carbons. That is convention for alpha rather than beta links.
Check out this picture, it is much clearer.
As you can see there are branch links which have the "extra" carbon because it is an alpha (1,6) linkage and there are the "chain" links which don't have the "extra" carbon because it is an alpha(1,4) linkage. The ones without the "extra" carbon do have the carbon, that carbon is in the ring. And that carbon 6, the "extra" carbon is on every single one of those glucoses... but there isn't a branch being formed off of every glucose.