I wrapped my IRC client (weechat + glowing-bear) in a Docker container. Oh, not a container though, because I also needed https, which meant I needed either a mechanism to build and update letsencrypt certs in the weird format that weechat expects, or to run an nginx instance in the front (and also somehow get the certs, but that's easier with nginx). So two containers.
And even though there was a ready-made nginx+letsencrypt https reverse proxy container (actually several), I had a huge amount of headaches to get it actually working. Even with the system set up, I occasionally have the container crash with exit status 137 (IIRC), which I've assumed might be because weechat leaks/consumes memory and eventually the host server kernel kills the process. Maybe.
So in my limited experience, comparing Docker containers to shipping containers is a gross simplification. Shipping containers are simple constructions requiring well-defined simple maintenance, while Docker containers seem to be complex thingamabobs that have multiple points of failure.