RZ5426 Wiring Harness

Needed to replace the wiring harness on my zero turn mower. So I looked up my model RZ5426, and the part number listed for this model was 580798101, so I ordered it. 

 
Found my manual today and looked in it, and the number it listed was 581091901.
 
Are these the same part? If not, which one is correct? What are the differences?
 
Both say they will fit the RZ5426 ZT mower. 
 
Thanks.  

Will have to check once the rain stops. But looking at the manual...its says its a RZ5426 / 967003602
 
And going by that number, this is what I got...
 

I appreciate the help you've given me.   I think the one I purchased will work.
 
I cropped just this section from the pic above.    
 

 

From looking at the schematic, the yellow wire terminates at the solenoid. Don't know what the red wire is for, or where the black wire with the large loop goes. Didn't see it on the schematic. 
 
Also, I don't think I'm getting power to the switch. Hour meter doesn't show anything on the display, and when I try to start the mower, it won't turn over, nor does the solenoid click at all. But, I can short out the top terminals on the solenoid and get it to turn over. It has a universal solenoid (has 2 tabs on the bottom as opposed to one on the original) Plugged the yellow wire to the tab on the battery side of the solenoid, and the other side I ran a wire from the second tab to ground. 
 
What am I missing here?  Which wire feeds power to the switch?