Regarding SSH, it has the advantage that you can (and should!) have multiple authorized keys for the same account. For example for the bastion host to connect to our VPC of servers we use individual SSH keys tied to the same proxy account. Databases generally don't allow that type of access.
Some allow using client certificates to login (which nobody uses). Some allow integration with external LDAP/AD (which very few use). The vast majority uses standard username/password based authentication that hopefully is going over SSL (seriously go and check ... for most DBs by default it's sent over plaintext).
Some places try to have per user database accounts (possible tied to AD/LDAP) but that usually devolves to the same app password sharing as the privileges aren't kept in sync or it's just too much of a pain to provision vs just giving someone the app password.