I've found a partial answer Difference between Minikube, Kubernetes, Docker Compose, Docker Swarm, etc here, but I still do not completely get it:
In my understanding, kubernetes is a container-orchestration system. However, Minikube looks very similar to me.
Can somebody explain me when you would use minikube versus when you would use minikube, and why?
I think your question should have been "Can somebody explain me when you would use minikube versus when you would use Kubernetes, and why?"
Minikube is a small and easy Kubernetes setup for your Work-PC. You can install and configure a Kubernetes cluster very easily with it. However, for a production environment it is not the best choice. Minikube normally starts a virtual machine on your PC witch will affects the performance of your cluster other than Kubernetes which will run directly with your kernel if you use linux. Furthermore, like Butuzov already answered, it is only one node, not a "real" cluster.
So you use Kubernetes if you are in a production environment where you need distributed systems and workload as well as redundancy and failure safety.
Hope that helps for your understanding.
Edit: Use cases
Minikube:
Kubernetes (standalone):
minikube - is one node cluster, with a master that can get loads, with a lot of solved and automated issues. designated to test, learn things from kubernetes ecosystem.
kubernetes itself is orchestrator that can come to you as managed service with a lot of problems (pv or loadbalancers) solved or like a lego, or you will tune here and there... well thing we called production ready.
minikube is ok to learn (not always but in 90% of cases) or experiment with tiny loads.