Yes, as was discussed before, Shop Parks in in the Parks division, and Disneystore is under DCP (Disney Consumer Products). So the basic line of products are totally separate. But then came some cross-boundary merchandising. Disneystore began carrying some items under the Disney Park product tab. Disneystore will carry items for awhile, and run various promotions and even put some on clearance, that is still full price at the parks. I assume they just need to move it out of the Disneystore warehouse. They also sometimes run "free shipping with at a park item purchase" promos.
Now the parks are carrying more and more DisneySTORE items, mostly "hardlines", toys (but not plush) and mugs. You will see these items at the parks, still with the Disneystore label on them (but possibly at a slightly higher price). The parks will even have some store items at full price, well after the stores have marked them down and sold out. I believe this trend will continue, cross-selling in both places. There were usually better prices on TDS.com, with sales, but the ShopParks app has sales too. I love having both options.
I do not think the stores have offered an AP discount, but they have offered a DVC discount, but I am not sure if they do online?