Ssh – How to disable sftp for some users, but keep ssh enabled

The first thing to do in this situation is to use the -v option to ssh, so you can see what types of authentication is tried and what the result is. Does that help enlighten the situation?

In your update to your question, you mention "on another local Ubuntu". Have you copied over the ssh private key to the other machine?

As I understand you have (at least for this particular problem) two distinct groups of users, one being able to login via SSH and get an interactive shell (let's call the group ssh) and one being able to login via SFTP and only get an SFTP shell (let's call the group sftp).

Now create the groups ssh and sftp on your system with groupadd, put the respective users in the groups (gpasswd -a $USERNAME $GROUPNAME) and append the following lines at the end (this is important!) of your sshd_config located at /etc/ssh/sshd_config:

Match Group sftp
  PasswordAuthentication yes
  # Further directives for users in the "sftp" group

Match Group ssh
  PasswordAuthentication no
  # Further directives for users in the "ssh" group

Read about the Match directive in sshd_config(5) and about the allowed patterns in ssh_config(5).

You'll also have to restart the ssh process for this to take effect:

sudo /etc/init.d/ssh restart