ASDM is the (optional) GUI tool used to configure and monitor an ASA. It is an application built using Java that can either be launched as a Java Web Start from the ASA or optionally be installed onto your local computer (via download from the ASA itself or by using the msi installer package from the downloads page). Either way it requires the binary image be present on the ASA if you want to use the GUI for management.
ASA software is the operating system of the ASA itself. It's roughly equivalent to IOS on switches and routers.
They are separately developed products and a major ASA release doesn't always require a major ASDM release to accommodate the new hardware support and software features, so the release numbering doesn't synchronize. There's a table here that lays out the compatibility between the two.
Hi Guys, I am curious what is difference between these two. One leads to version maxed out at 7.x and other at 9.x. Please let me know. 
