I am not a fan of carts with the rear half swapped out. People often do this if the back label was damaged, to make the game look new.

I recently bought a copy of Ninja Warriors locally, and the rear half looks significantly different from the front half. I'm wondering if the back was swapped. Can someone look at the rear label of their cart and tell me what number is "stamped" into the label? The number should be the same on every cart for this game.

Yes, most likely it was since it's a decently priced game and for resale value, a nice back would make it more desirable. Most resellers will do this to good games cause it only takes 1 min worth of work. The backs are universal for the most part so it doesn't matter really either.

I notice that the plastic on Super NES games will often discolour differently on the front and back half. Even NES games have this sometimes. So, the difference I see between the two halves could be perfectly normal. I am fairly certain my game still has the original back, but I would like to confirm.

No, it's not normal. Discoloration between the front and back 99% of the time means the back was switched out. It's normal in the fact that this happens all the time, but not normal meaning it doesn't happen naturally. Just get yourself some NES/SNES/GB screw bits and switch the back out yourself. It's super simple. You should be cleaning the contacts on your personal games anyways so learn how to do that and start taking all your games apart. Then just switch out a shit title with a good back for the back of your Ninja Warriors and your good to go. Use Brasso with a qtip to clean the grim, windex or isopropyl alcohol to wipe it off.