You really do not want to use a relative path here - it is just that: relative to the current location.
If you store these images in a directory below the location where the application resides, then specify that folder absolutely:
btn_Stop.Image = Bitmap.FromFile(Application.StartupPath + "\\Image\\btn_Stop.Image.jpg");
btn_Start.Image = Bitmap.FromFile(Application.StartupPath + "\\Image\\btn_Start.red.jpg");