I will try to provide a little more info...
Bike 1 was a six-speed folding bike. It had:
- A Shimano indexed shifter. I couldn't see a model name or number other than "SIS Indexed". It has the grey button for down shifting and the black lever for up shifting.
- A standard width six gear rear cassette. I measured about 1 1/8" width from top to bottom gear. Smallest gear has 14 teeth, biggest has 28.
- A short-cage shimano rear derailleur. All I sse on it is "Shimano SIS".
Bike 2 is an 18 speed Miele mountain bike. It had:
- Old-school handle mounted shifters. Not indexed, but they do "click" as you turn them, if that means anything.
- same width (1 1/8") rear six gear cassette. smallest gear has 15 teeth, largest has 36.
- A long-cage Shimano rear derailleur. Again, I couldn't see any other model name or number on it.
So far what I've done is to take the indexed shifter from bike 1 and put it on bike 2.