IAAS = Infrastructure-as-a-service.
PAAS = Platform-as-a-service.
With IAAS, Azure provides the virtual machine, but you are yourself responsible for maintaining the machine, that is patching of operating server, applying cumulative updates for SQL Server etc. You will also have to arrange for backups of database, rebuild of indexes etc. If you want HA, you need to set up that yourself.
With PAAS, Microsoft manages the entire platform, and you have no control over when the operating system or SQL Server is upgraded. Azure takes backups. The service can also automatically and indexes it thinks it may be useful. But since your system better, you can do this part better yourself.