Confused
I sure don't understand cryptocurrency at all
Cryptocurrency: A virtual currency that has no central bank or authority controlling its supply.
There are two main differences (The mining might explain this better) Script coins (Litecoin and dogecoin) and Coins that use use SHA-256 (Bitcoin). Those are just different algorithms.
Why should you mine? Because it helps verify payments and keep the whole system secure, and you get to earn free coins while your doing it.
Hope this helps a bit.