Why doesn't every successful trade appear on the Level 2 order book?

I have noticed that not every successful trade appears on the Level 2 order book. Particularly for illiquid shares. Take the example below, where the book is filled with Market Makers. A lot of the successful trades made (Trades section) don’t ever show on the book. My initial understanding is that the trades that never appear on the book are OTC orders and are only made "public" once they’ve actually been transacted, rather than the facilitators publicly disclosing their intentions prior to a deal being made. That said, I’m not 100% sure if (a) this is true or (b) if there are other types of orders that may never appear on the book but will appear as a successful trade.