Difference Between Database Mail Profile and SQL Server Agent Operator in MS SQL Server
I believe Database Mail profiles are purely for the set up of what mail server to use and what email address the emails appear to be sent from.

SQL Server Agent Operators are essentially user(s) who are able to receive notifications of job statuses, effectively the receivers of email.

So Database Mail is for sending email, Operators is for receiving email.

https://docs.microsoft.com/en-us/sql/relational-databases/database-mail/configure-database-mail?view=sql-server-2017

https://docs.microsoft.com/en-us/sql/ssms/agent/operators?view=sql-server-2017

Note on this link https://docs.microsoft.com/en-us/sql/relational-databases/database-mail/configure-sql-server-agent-mail-to-use-database-mail?view=sql-server-2017 it discusses setting up Database Mail for use in SQL Server Agent and it lists setting up the operators as a follow up task.