So let's say you apply for a Chase Business Card and are approved.
The inquiry (hard pull) will show up on your Personal Credit Report (in my case, Equifax). However, the new card account doesn't show up on ANY personal credit report (thus, you "stay under" the Chase 5/24 rule). MOST business credit cards don't show up on your PERSONAL credit report (there are a few exceptions but Barclays, Citi, Amex, and Chase don't show up on personal reports). But when you are seeking credit, the inquiry WILL show up (again, Amex is a different animal as typically if you have a credit card with them already and apply for another Amex card, they "generally" don't do a hard pull on your personal report).