If you go to the official documentation and see what are the components within a LoRaWAN architecture, can you visualize that there are two main entities that standout, the Sensor and Network Server.
LMIC libraries are pieces of code that you can use on the Sensor side to provide LoRaWAN capabilities to an end device, in this sense, making them able to communicate with the Network Server. On the other hand, what Chirpstack does is taking care of all the complex tasks that you need to do if you opt to manage a private Network Server, this means that, Chirpstack resides on the Network Server side and some components are withtin the Gateway Host as well.
To close the loop in this context, LMIC libraries are not the same than Chirpstack ecosystem. Both can be part of a LoRaWAN infrastructure but are located in two different regions.
Hope that helps,