If you believe "The magic Pudding" is a refference manual rather than an item of childrens fiction then the blind answer is no they are exacty the same.
However if you live in the real world you will understand that there is a finite amount of profit in making a product that can be dipped into to provide merchants mark downs.
Then we have cost efficiencies in scale so making 100,000 units can end up being 10% cheaper per unit than making 50,000 units however this can also go backwards once you have surpassed your most efficient production volume.
Then there are other costs. It is a lot cheaper per unit to send a full trailer load of mowers to a bulk distribution centre than it is to send 1 to a dealer.
Then there are finance costs, dealers get somewhere from 60 to 120 days free credit to pay for the mower so hopefully you pay for it before the dealer has to pay for it.
Big box stores usually pay on 30 to 60 days so JD gets more money faster so reduces their borrowing costs and these are astronomical for makers of highly seasonal products.
SO some companies can sell to big box identical products at the lower prices the big box will pay.
However usually the manufacturer will find some cost efficiencies or build down to a slightly lower spec and this is nearly always the case with lines that are exclusive to big box stores.
The amount that JD can tamper with the quality is proportional to the cost of making the modifications at the production line.
While you can save money by fitting say a cheaper starter motor, there is a cost associated with changing, ordering smaller quantities, adding another inventory line to your warehouse then the paper trail so some times it is not cost efficient to drop the specs.
This is what Honda claim for their walk behinds sold by big box companies and it may well be true.
OTOH common little tricks can be applied like pressing the parts out of slightly thinner steel which can increase the die life up to 60% which in effect knocks 30% everything that has come out of that press. Press dies can go anywhere up to $ 500,000 a set. So getting more out of them makes a big difference to the bottom line and is virtually undectiable by the purchaser, particularly if the part made from the thinner steel get a nice heavy powder coat so it feels thick between your fingers. I see this 5 years latter on where all the pivot holes get flogged out oval.
You see this with identical looking mowers branded differently and is easiest to detect by looking at the weights.
Check out the specs of each diffeent branded owed that comes out of the AYP tractor factory .
Price reduces proportionally with weight reductions.