I did a casear analysis and found that the theoretical installed load in
hanger table report obtained is not matching exactly with the Fz load in
sustained case, why is it so? However both are comparable but as per my
understanding they shoud match exactly.

Read the section in the Technical Reference Manual (Chapter 6) on hanger design. The theoretical installed load is purely a "theoretical" load computed based on the outcome of the hanger design - without the spring in the system.

The Sustained case on the other hand, has the hanger installed in the system. As a result, the stiffness of the spring may affect the final load distribution on the supports.

I could quibble with Rich's response...

The spring rate alone does not affect the sustained case loads. It's the preload that does the work here. Normally, the load is balanced in the operating case (hot load design) so the load in the cold case, with its different vertical position, is out of balance. It is this out of balance load that causes the different numbers. These differences are usually low and any large difference would indicate a high load variation on the spring or a very "sloppy" (flexible) system with respect to the magnitude of the hanger load.