'Turn into' focuses on a change from one thing to another. 'Make into' focuses on what the person does to change this thing. 'Make into' can only be a transitive verb. Or in other words, it has to have an object. 'Turn into' can be transitive or intransitive. For example, you can say: 'I made the wine bottle into a pretty candlestick' or 'I turned the wine bottle into a pretty candlestick' If the meaning is intransitive (no object) you have to use 'turn into'. The caterpillar turned into a butterfly. The plain little girl turned into a lovely young woman.