true, most of the time…
Basically I agree that it shouldn’t make any difference, but once in a great while it does matters.
For example, if you are barely over the price to qualify for a store special (e.g.. buy $15 on frozen food, get $5 off).
In that case you would want to first use the store card, to knock it from $15 to $10, then you can use your coupons for the individual products next. Otherwise, your coupons may lower your total below the $15 original required purchase.
Most of the time it doesn’t matter. However, as a habit of mine I like to wait until after they ring up everything before giving either, to see how much they think all that stuff is supposedly worth.