I think people talk about a 'rendition' of a book or a song/play (in a different language/way) ('performance' would be 'weird' in that sense) to mean a different interpretation/arrangement/emphasis. A new rendition can be performed...

Please see Wordnet (3.0) for many different meanings of verb 'render' and note the frequencies of intended meanings. viz

1. cause to become (Freq. 12)
- The shot rendered her immobile

2. give something useful or necessary to (Freq. 10)
- We rendered the room with an electrical heater

3. give an interpretation or rendition of (Freq. 4)
- The pianist rendered the Beethoven sonata beautifully

4. give or supply (Freq. 2)
- The estate renders some revenue for the family

...

6. make over as a return
- They had to render the estate

On 'relation' we hear a lot of the phrase 'no relation' eg. John Smith says things abour Bill Smith and mentions that he is 'no relation' to Bill (properly he and Bill are not relative).