Oh yeah, this is very different. The traditional approach will not work with Azure, at all.
Now, the question I would have is, are we talking about migrating between Azure environments or are you talking about moving a database from a traditional SQL Server instance to Azure SQL Database? If we're talking the former, it's just a question of scripting the security and then migrating that to the new location. The database itself can be moved through a bacpac process, although you should only do that from a copy of the database in order to avoid issues with active transactions.
If we're talking moving from an instance to Azure SQL Database, then you have a bunch of work in front of you. Most importantly, there are no cross database queries, so any of those in your code have to go. There are also a few things unsupported in Azure SQL Database (CLR for example, there are others), so make sure you're not using those. Again, no backup & restore, so you have to look to bacpac. SQL logins or Azure Active Directory are supported. If you don't have AAD configured (and hooked into your local AD), you'll have to do that first.
This is a big topic. I'd suggest looking to the Microsoft documentation on the topic. There's a lot of it.