Chainsaw Repair

Hello, new member looking for some hand holding / advice re parts to repair my Poulan Pro PP4218A.
Purchased new, came with a case, spare chain etc., for some light work around our yard, my first saw. It was difficult to start and not much power. Started looking for reason and found the fuel line was coming apart at the pick-up. Replacing that made a huge difference, then I adjusted the carb mixture screws and attacked an old apple tree, it was running and cutting 110% until it seized!
Guess it was too lean.. so a new cylinder and piston is needed to put it back together again; this will only happen if I use cheap aftermarket / ebay parts.
My question is: There are 2 listed that look like mine, same bore etc., no visible differences to my eyes, but different part numbers, and of course prices. The cheaper one is:
530071885, listed for a McCullough and a Partner - which I would like to buy.
The other is listed for Poulan
530071884
Reading the Poulan history article I noticed that Poulan and Partner are in the same “family”, and having a manufacturing background I suspect that it is unlikely there would really be different parts that close to being the same, just a number difference for pricing etc., hoping anyway.
Also hoping that someone can confirm that for me.
Many thanks, Trevor

Thank You Cut4fun, think I will be ordering the cheaper chinese kit for now, just hope I can remember how it all goes back together.
Appreciate the offer of your parts, might regret...
Cheers