Observability is the capability of knowing what's going on in a live system. We can deal with low-observability systems, where we have no way of knowing what's going on, or high-observability systems, where we can infer the events and internal state from the outside through tools.
Observability is a property of the system itself. Typically, monitoring is the action of obtaining information about the current or past state of the system. It's all a bit of a naming debate, but you monitor the system to collect the observable parts of it.
For the most part, monitoring is easy. There are great tools out there that can help us capture and analyze information and present it in all kinds of ways. However, the system needs to expose the relevant information so that it can be collected.
Exposing the correct amount of information is difficult...