Michelson: Parameter vs Storage

The difference is very simple :) The parameter is made of data that are sent to the contract with a transaction while the storage holds the state of the contract (i.e all the data that the contract saves to be reused later). It is true that both the storage and the parameter can be seen as inputs because they are fed to the contract at the beginning of its execution, but the parameter comes from the "outside" while the storage comes from the "inside".
The initial storage value is the one passed to the contract at the beginning of the execution and the final storage value is the one generated by the contract. If you have a contract that adds a number sent in the parameter to a number in the storage, let's say 5 in the parameter and 6 in the storage, the initial storage will be 6 but the final storage will be 11. If you send another transaction with 4 as a parameter, the initial storage will be 11 and the final storage will be 15.
Finally, the storage can hold any kind of value you need, from simple ones like int or timestamp to more complex ones like pair or big_map.