What is the difference between Clean-room and sterile-room?

You may want to double-check this, but I believe PCR-clean simply means that there are no DNases or RNases on the item, but they still could have nucleic acid on them. Essentially there is nothing on them that would interfere with nucleic acid amplification achieved with PCR, but any genetic material they may have will be amplified.

Sterile means that there is absolutely no genetic material on the item itself (usually achieved via autoclaving where the temperatures climb so high that they would denature the DNases and RNases anyway).

Nutshell: PCR-clean = wiping with RNA away and DNA away

Sterile = bleaching and autoclaving