Can you explain the difference between the Mini Private key and the Full-size Private key?
Almost any integer between 1 and 2
256 can be turned into a full-size private key. A big difference of mini private keys with other formats is that, not every 256-bit number that can be encoded in a full-size private key can be encoded in mini private key format too.
The other difference I know is that there is no way to convert other formats of private keys to a mini private key.
Is this something like a URL shortener where you make it easier for people to remember the Private Key?
A mini private key (even the shortest format which includes 22 characters) is still difficult to be memorized.
A mini private key can be used when there is no enough space for writing a full-size private key.