As the graph shows above. Which type of sql server edition is for the production? I know the "Developer" version is for the development. Also I already got the Azure VM and have the "Developer SQL Server" on my VM, how can I install the production SQL Server in my VM? Is this free?
My purpose is to make a production SQL Server database. Is there two options for me? One is install a production SQL Server in my VM, another is to create a new Azure SQL database. Which one would be the best way to do this?
As the graph shows above. Which type of sql server edition is for the Production? I know the "Developer" version is for the development. Also I already got the Azure VM and have the "Developer SQl server" on my VM, how can I install the production sql server on my VM? Is this free?
Developer is not licenced for production - you aren't allowed to use it for production purposes.
Express is licenced for production but if your database gets bigger that 10Gb then it is unsuitable for your use
My purpose is to make a production sql server database. Is there two options for me? One is install a production sql server on my VM, another is to create a new Azure SQL database. Which one would be the best way to do this?
"Best" doesn't mean anything. What are your constraints? Are you creating a brand new database? What tools will be connecting to and using the database? Does it need to be accessible from the internet?
If this is a brand new application / database, and you have limited capability for maintaining a VM then I definitely recommend using SQL Azure instead of a VM
Most importantly, and based on you other question, make sure you understand the term "Production"
Can Azure SQL Server on VM be the production database?
For example, you usually don't provision a 'production' environment without also provisioning at least a dev environment.
It would also help to give us some background on "My purpose is to make a production sql server database". It sounds like this is a request someone has given you but maybe you don't fully understand the term 'production'