Separate SQL Server or just separate SQL Database for test and production?
Go with a separate logical server:


It is going to cost the same because you are charged on the tier of the database not the database server.
By providing separate servers you provide isolation between the two databases protecting one from the other. 
Unless​ you use contained users your users will be shared between Test and Production, if you happen to use the same user for both databases a change of the password in production would also require the same change in Test.


You might want to use the same server for a database if:


You are creating a very large number of Databases across many Dev/Test environments as there is a limit to the total number of SQL Servers. 
You have two databases that need to be deployed as part of the same ARM template.