what is the solution to host their existing SQL Server Integration Services (SSIS) packages ? ( migrate their on-premises Microsoft SQL servers to Azure).

 Azure Data Factory for hosting the packages.

Architecture of SSIS on Azure:

what is the difference b/w SSIS ON prem and SSIS on Azure ?

The most significant difference is the separation of storage from runtime. Azure Data Factory hosts the runtime engine for SSIS packages on Azure.

The runtime engine is called the Azure-SSIS Integration Runtime ( Azure-SSIS IR ).