Help with what exactly is primary succession?

Let's take for example, the example I was studying off of a Khan Academy article, it says:

"First, weathering and other natural forces break down the substrate, (rock) enough for the establishment of certain hearty plants and lichens with few soil requirements, (pioneer species). These species help to further break down the mineral-rich lava into soil where other, less hardy species can grow and eventually replace the pioneer species. In addition, as these early species grow and die, they add to an ever-growing layer of decomposing organic material and contribute to soil formation."

Now this is where I'm confused, I'm wanting to know if primary succession just describes that first "layer" of pioneer species or if primary succession is the form of succession where organisms will colonize newly exposed environment, meaning this next part would be still a part of the primary succession (going by the latter definition) but this next part would NOT be a part of primary succession going by my first definition. unclear on that distinction.

"This process repeats multiple times during succession. At each stage, new species move into an area, often due to changes to the environment made by the preceding species, and may replace their predecessors."

So basically does primary succession encapsulate both the paragraphs (basically describes all of the succession that occurs when you have newly exposed, habitat environment) or does primary succession just encapsulate the first paragraph (that is, such a concept only refers to the FIRST change in a newly habitual environment).

Personally I'm leaning towards the first definition/understanding as that is more consistent with the definition of succession but I just wanted to double check!

I can't add a link for my first post but this information is from the Khan Academy article "Ecological Succession".