Yes , a small changes in a design can change the sound !  Th
Yes , a small changes in a design can change the sound !  The best way to realise this is to try : 
Build two small identical devices  with different  ( pin to pin compatibles) opamps ... Say for example  a simple stero line preamp ( 2 single inverters  in serie with  10K1% resistors everywhere...)  Then perform A/B tests to compare, at the same level if possible ...If you monitoring system is good enough -Forget your PC speakers to do that - you should hear a difference , at least between someting like a 741 and an OPA604 ! 
 
It is  just an example ...  
It happen often when you compare AB two  2  identical vintages devices that they have a different sound !  A lot of famous Roland drumboxes are like this  but not only ... I saw this on many vintage Mutron Biphases , many old synths too ...  The sound is very close , but not exactly the same due to parts age, repairs, but alos sometime to differences who exist since the day this device went out of the factory ! Never forget that all parts have a % range of error and that nothing is perfect in analog domain . So there is always a difference even on the most accurate analogue circuits !
   
>I hear from some guys that even the board or layout can change the sound >results..
Yes:
1) each track is  like a very low value resistor , but never zero ohms .
2) Two tracks nearby compose a small capacitor ... 
3) The pcb material ( epoxy, fiberglass, bakelite, etc  ) have a huge resistivity , but none is a perfect isolator between tracks ...
All those small "parts" can  have an big influence. It depend a lot of the device you design ...
This kind  of things is generaly more sensitive on HF circuits but it can be audible on audio designs too ( mic pre, etc )  or alterate perf ( ie: SNR, stability ...)  
 
A pcb can be good or not  only because of the layout ... There are many "rules" a designer should follow to make a good pcb, ie : keep signal path away from psu rails, draw ground as a star to avoid loops etc ...