Entering a guilty plea to a lesser charge does not necessarily mean you are not guilty of the original charge.  A criminal charge has various elements in its definition that need to be proved beyond a reasonable doubt to obtain a conviction.  You may have been offered the plea bargain to a lesser charge because the prosecutor had a stronger case for establishing guilt beyond a reasonable doubt by proving all of the requisite elements of that lesser charge than of the original charge.  It is also possible that you may have been offered the plea bargain to a lesser charge for other reasons such as your cooperation in testifying against others  or that this was your first offense or obtaining a guilty plea on a lesser charge saves the time and expense of trial, etc.  There are numerous other reasons why you may have been offered the plea bargain on a lesser charge.  There is also the possibility that not pleading guilty to the lesser charge might result in prosecution on the original charge.