After hours service is rather self-explanatory, but a hot shot is not such an evident term for those not familiar with the service. Simply put, a hotshot is when you need a delivery picked up and delivered as fast as possible.
You are searching for a courier company that works after regular business hours, and can also provide delivery service on a moment's notice when you have those urgent "fires to put out." How do you know how find one that you can count on for such critical needs to serve your customers?
The obvious is to look for one advertising that they provide 24/7 courier service, 365 days a year. The not-so-obvious is how your call is handled by those that state they cater to these emergency situations.
Try calling them after regular business hours to see what kind of actual live response you'll get in your search. They may only have an answering service during those hours, and you'll be wasting precious time waiting for their response.
How do you know that you have only reached a call service? They may state that they will have someone return your call shortly, and not take all of your pertinent information immediately.
You want to make contact with a knowledgeable human being on the other end of the line who works for the company, not a person that's simply taking messages for them after hours.