Unicode is a standard and about UTF-x you can think as a technical implementation for some practical purposes:
UTF-8 - "size optimized": best suited for Latin character based data (or ASCII), it takes only 1 byte per character but the size grows accordingly symbol variety (and in worst case could grow up to 6 bytes per character)
UTF-16 - "balance": it takes minimum 2 bytes per character which is enough for existing set of the mainstream languages with having fixed size on it to ease character handling (but size is still variable and can grow up to 4 bytes per character)
UTF-32 - "performance": allows using of simple algorithms as result of fixed size characters (4 bytes) but with memory disadvantage