Order entry software is the layer that turns a customer's order into a record in your system without a person retyping it. That is the whole job. Everything else a vendor puts in the brochure sits either side of it.
The reason the category exists is that B2B buyers do not check out. They send a purchase order, and they send it the way their own procurement process demands: a PDF from their ERP, a spreadsheet a buyer maintains by hand, a few lines in an email body, a scan of a signed form. Your catalogue is structured. Their document is not. Somebody has to bridge that, and for most wholesalers that somebody is a person on customer service with a Shopify tab open on one screen and a PDF on the other.
For a Shopify wholesaler, the practical definition narrows further. Good order entry software writes a Shopify draft order, matched to the right customer, priced from your catalogue rather than from the buyer's document, with a human approving before anything is committed. If it writes anywhere else, you have bought a second system of record and inherited a sync problem.