Series connection- The electrical components(R,L and C) are connected back to back such that the current through them is same.
Whereas in cascade connection the output of one block is fed to the input of 2nd block and output of 2nd block is fed to the input of 3rd block and so on. In this connection a block may contain series or parallel connection of R,L,C or may be any other devices as well. Generally, this connection is done to amplify the voltage level after each block like multiple transistors are connected in cascaded connection to amplify the signals after each block.