What are the inner and outer markets?

I found a lot of explanations online, and it feels like none of them are right. For example, the following: [Taoguba]

But it doesn’t explain why they’re called the inside and outside market—why can’t they be called the other way around?

My own understanding is also relatively easy to remember. Interpret “inside and outside” as holding stocks and holding cash/coins. Those who are already in the game—that is, in the order book—are the inside; those who are outside the game—that is, holding cash/coins—are the outside.

Whoever is the one initiating is “their” market. Initiation from the outside is the outside market; initiation from the inside is the inside market.