Meterpreter and staged payloads

So starting with the absolute basics - an exploit defines how attacker will connect/take advantage and deliver payload to victim machine right?

A staged payload creates a connection to a victimes machine using a stager - which is a small initial payload that creates a connection to the victim (creating a stager socket) and then passes execution to the next stage which will be the main payload - in this case meterpreter.

In this context, meterpreter is a payload that will be loaded through the stager socket and will allow dlls to be injected to victim machines (meterpreter server) memory...

I've done some research and for me to understand things I attempt to put them in my own words and terms as much as possible.. This is my basic understanding of how staged payloads and meterpreter works, so can you please clarify that my understanding is actually correct?