Axis letters vs joint numbers - does the order matter?

KINEMATICS_TYPE kinematicsType()
{
    static bool is_setup=0;
    if (!is_setup) polar_userkins_setup();
    return KINEMATICS_IDENTITY;

if (switchkins_type == 1) 
    {
        // G12.1 mode : do polar to cartesian conversion
        angle_rad = j[2] * M_PI / 180.0;    
        radius = j[0] - tool_offset;
        pos->tran.x = (radius * cos(angle_rad)) + tool_offset;
        pos->c = -(radius * sin(angle_rad));  // ref comment in inverse kinematics        
    }
    else
    {
        pos->tran.x = j[0];

        // on an exit from polar, am adjusting the pos->C and j[2] values so that the max distance back to zero
        // will be between 0 and 360deg. As in polar mode, we may have clocked up several revolutions of C, which 
        // means if did not do this setp, would unwind all these positions. The method is derived from what the 
        // caxis component does on a transition from spindle to caxis mode. Note that the j[2] value is updated 
        // in the caxis component as cannot write associated net pin here as that pin is written to in caxis.
        if (prev_switchkins_type_fwd != switchkins_type)  
        {
           offset = round(*haldata->spindle_revs);
           pos->c = (*haldata->spindle_revs - offset) * 360;                     
        }
        else        
            pos->c = j[2];
    }
    prev_switchkins_type_fwd = switchkins_type;
         
    pos->tran.z = j[1];
    pos->b = j[3];   
    
    // unused coordinates:
    pos->tran.y = 0;
    pos->a = 0;
    pos->u = 0;
    pos->v = 0;
    pos->w = 0;

    return 0;