Using SQL Server Management Studio to remote connect to docker container

connect via SSMS using the public IP address, followed by comma separator and then the port (,port)

You'll also need the sa credentials to make this work.

In your case, Server Name input will become Server IP, port#

Remote setup image

No need of ssh, you just need to expose SQL Server service to the internet.

When Using SQL Server Management Studio to connect to the docker container on local machine, you can use localhost ip. In that case Server Name input will become,port#

To clarity, I attached image of my SSMS Connection Dialog