The Hilton website carries mentions of both Business Centres and Business Corners in the description of its hotels. My understanding, from a quick search, is that the difference between these is likely to be the size of the allocate space, and the number of machines available. Just as an example, below is a picture of the Business Centre at the Hilton Malta:
Compare this with a picture of the Business Corner at the
Hilton Garden Inn Rzeszow (from tripadvisor):
For completeness sake, note that the Hilton Opera website mentions a 24-hour complimentary Business Corner in its amenities description.
The business centre is an area with some desks, computers and a printer. Often there is a copier and fax device as well. You can access the internet, print documents, scan receipts and so on. The facilities vary a little bit from hotel to hotel. Often it is next to the hotel lobby, and not very private.
Usually the business centre is not very busy, because most business travellers will have a laptop.
If you go to a hotel without a dedicated business centre, the front desk will usually be willing to print documents for you.
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