Online stores
Online store surveys
In an online store the hard part is not getting responses, it is knowing what you are measuring. Ask before the parcel arrives and you measure the anxiety of waiting; ask about "the order" in general and one bad courier sinks the score of a product that was perfectly fine. Split product and delivery into separate questions, send once the carrier marks the parcel as delivered, and make the open text conditional on low scores, because that is where the reason lives.
The templates
Wait until the parcel arrives
The post-purchase survey is not triggered by the payment, it is triggered when the carrier marks the order as delivered, and better still one or two days after that, once the person has opened the box and used what they bought. Send it earlier and you are asking about an expectation: people will answer about the promised delivery date and the nerves of not knowing where the parcel is, not about the product you wanted to evaluate.
Product and delivery, asked separately
A crushed box or two days of delay contaminate the rating of the product itself, and then you spend weeks arguing about whether the problem was the catalogue or the logistics operator. Ask twice: once about the item (quality, whether it matched the photos, whether the size or the measurements were right) and once about the delivery (timing, condition of the parcel, the courier). With two separate scores you know who to call, and you can change carrier without touching the catalogue.
The survey for people who did not buy
Of the four, the abandoned cart survey is the only one you send to someone who did not buy from you, and it is the one almost nobody sends, for fear of being a nuisance. It is also the most profitable: whoever reached the cart already wanted the product, and the reason they left (shipping costs that only appear at the end, being forced to create an account, doubts about returns) is usually something you can fix this week. Send it within 24 hours, with no discount attached.