Let's start with clarifying the terminology:
Grid Container
The grid container is the overall container for the grid and grid items. It establishes the grid formatting context (as opposed to another formatting context, such as flex or block).
Grid
The grid is a group of intersecting vertical and horizontal lines that divides the grid container’s space into grid areas, which are boxes that contain grid items.
Grid Items
Grid items are boxes in a grid container that represent in-flow content (i.e., content that is not absolutely positioned).
Here's an illustration from the W3C:

The justify-content
and align-content
properties align the grid.
The justify-self
, justify-items
, align-self
and align-items
properties align the grid items.
With regard to the problem described in your question:
My confusion revolves around the claim made by the author that the "-content
" set are there because: "Sometimes the total size of your grid might be less than the size of its grid container"
Well, you can see in the illustration that the grid is smaller than the grid container.
As a result, there is space remaining and the container is able to distribute this space to vertically center (align-content: center
) and right-align (justify-content: end
) the grid.
The extra space could also allow the grid to be spaced apart with values such as space-around
, space-between
and space-evenly
.
However, if the grid size equaled the container size, then there would be no free space, and align-content
/ justify-content
would have no effect.
Here's more from the spec:
10.3. Row-axis Alignment: the justify-self
and justify-items
properties
Grid items can be aligned in the inline dimension by using the
justify-self
property on the grid item or justify-items
property
on the grid container.
10.4. Column-axis Alignment: the align-self
and align-items
properties
Grid items can also be aligned in the block dimension (perpendicular
to the inline dimension) by using the align-self
property on the
grid item or align-items
property on the grid container.
10.5. Aligning the Grid: the justify-content
and align-content
properties
If the grid’s outer edges do not correspond to the grid container’s
content edges (for example, if no columns are flex-sized), the grid
tracks are aligned within the content box according to the
justify-content
and align-content
properties on the grid
container.
(emphasis added)