Both are ways to manage containers, and both can use the same container runtime provider, IIRC.
They are different in how they manage the containers, with docker/docker-compose being suited for development or one-off services, and kubernetes being more suitable for running and managing a bunch of containers in production, across machines, etc.
Think of kubernetes as the pokemon evolution of docker.
I did come across it before, but it feels like just another layer of abstraction over k8s, and with a smaller ecosystem.
Also, I prefer terminal to web UI.
Setting up k8s with k3s is barely two commands.
Works out of the box without any further config.
Heck, even a multi-node cluster is pretty straightforward to setup. That's what we're using at work.
Several services are interlinked, and I want to share configs across services.
Docker doesn't provide a clean interface for separating and bundling network interfaces, storage, and containers like k8s.
I used docker for my homeserver for several years, but managing everything with a single docker compose file that I edit over SSH became too tiring, so I moved to kubernetes using k3s. Painless setup, and far easier to control and monitor remotely.
The learning curve is there, but I already use kubernetes at work.
It's way easier to setup routing and storage with k3s than juggling volumes was with docker, for starters.
Both are ways to manage containers, and both can use the same container runtime provider, IIRC. They are different in how they manage the containers, with docker/docker-compose being suited for development or one-off services, and kubernetes being more suitable for running and managing a bunch of containers in production, across machines, etc. Think of kubernetes as the pokemon evolution of docker.