[spondylosaurus]

Do these stores' checkout pages have a section to enter your billing/shipping details on the left, and then a pane displaying what's in your cart and any active coupon codes on the right?

If so, it's almost definitely Shopify.

I know what checkbox you're referring to, and another fun thing is that if you use PayPal (or, I assume, another non-credit card payment method), it bypasses the "Sign me up for promotional emails" checkbox entirely... but it still checks it for you.

So if I check out with PayPal I have to select the PayPal option, sign in to PayPal, confirm, then in the store's checkout page go back a page to manually uncheck the box. Drives me crazy. Unchecking it beforehand does nothing.