There are cases where cmdlet names and parameters have changed significantly and geo-replication is an example of that. With ASM one would use Start-AzureSqlDatabaseCopy while New-AzureRmSqlDatabaseSecondary must be used with ARM.
What follows is a comparison on how you can enable geo-replication with ASM vs ARM.
If you would like to know more about the differences between ARM and ASM please follow this link.
Enabling Sql Server Geo-Replication With PowerShell (ASM)
Enabling Sql Server Geo-Replication With PowerShell (ARM)