The swap that looks close
a rigid carton is the usual substitute for grey mailing bags, and it is the wrong one. A carton is for goods that must not be crushed. A mailer will not do that job.
Wholesale Packaging lists Mailing bags separately because the jobs diverge as soon as the goods are on the bench.
What the right line actually does
Grey mailing bags are for soft goods that do not need a rigid wall.
The category calls them shoe bags or grey mailers. They are opaque, European made from a blend of recycled film, and described as 100% recyclable.
If you have already mixed them
Posting a fragile hard item in a mailer because the right carton is out is the failure.
A Wholesale Packaging basket with Mailing bags still leaves the same day if it is placed by 3pm. The terms aim for 5.30pm the next working day. A 1 to 3 day courier is also described, depending on the lines.
Open Mailing bags when you already know this line. Bags are pack quantities. Read the count on the product before you assume a single bag. Wholesale Packaging will still dispatch an order placed by 3pm on the same day.