> I also have read many times that Walmart forces manufacturers to cut quality to meet certain price points for products sold in their stores, whereas I haven't heard anything like that about Target.
This is less insidious than it sounds. Walmart's strategy is a volume play - they optimize their product mix against selling the highest volume of products, rather than products that may have a higher individual margin but lower sales volume.
They're also intimately familiar with the elasticity of price for everything they sell. If a manufacture comes to them with Product A, Walmart won't purchase Product A if they can't price it at the optimal point for their target market (which encompasses a large cross section of the general population). But their procurement volume is so high that they can commit to absurdly large order quantities. So instead of just walking away, they'll work with the manufacture to comb through the bill of materials[1] and adjust things such that a Variant B of Product A can be produced more efficiently or cheaply, then sold to Walmart at a wholesale rate that allows them to hit their target retail price. This can be as simple an adjustment as reducing a 3 year warranty down to a 1 year warranty. Or swapping out a fragile but sleek looking component with a more robust but worse looking (or heavier) component, thereby reducing expected warranty claims and overall product cost. Or if they feel a particular component is likely to not be used by 90% of their purchasers (i.e. a marketing gimmick the manufacturer threw in for differentiation) they'll ask for it to be removed. Or if a particular component is overbuilt for their audience they'll ask it to be swapped out with a lower quality component (keeping in mind that Walmart has lots of data from returns to understand what does and doesn't work well). Or it could be a feature that is turned off/disabled to give the manufacturer cover for selling (and letting Walmart sell) the product below the equivalent product sold to other retailers.
Keep in mind that returns and warranty claims all cost money, as well. And at the volume of sales Walmart has, even minor increases in these can have very noticeable increases in costs/decreases in profitability and negate the entire benefit of creating a new product variant to hit a specific price point. So in that vein, you can be sure that the new variant will meet the consistent quality expectations of products purchased at Walmart, even if they don't necessarily meet the quality expectations you might have of purchasing that brand elsewhere. It's basically a private label product commissioned by Walmart that still happens to have the manufacturer's brand name attached to it.
Target and other large retailers do the same thing, they just don't necessarily have the volume to have enough leverage to get manufacturers to do it on as many things as Walmart does, nor the internal competencies to do it at such a deep level. They also have different points of price sensitivity for products, based on the particular demographics of their consumers. You're more likely to see fuzzying around with quantities/volumes instead, since the primary manufacturing run is the same and you only require a custom pack during final packaging.
And to that point, manufacturers do the same thing themselves frequently. Consumers are price sensitive and manufacturers for years have been absorbing price increases on raw materials while maintaining price points. They do so by either maintaining the same quality of individual units and just silently shaving off quantity, or else decreasing the quality and maintaining quantity. These changes usually come along with refreshes/redesigns of product packaging, in an attempt to mask them from notice.