Hi all!
I deal quite a bit with international pet shipping to/from the Asia-Pacific and thought I'd try to clear up some of the terminology here. It can be quite confusing.
"Manifest cargo" simply means you are sending your pet from point A to point B, underneath the plane, "consigned' to someone on the receiving end. HK requires that all live animals arrive as manifest cargo no matter where they are coming from. The "consignee" can be anyone -- you, a relative, a professional pet transportation company, a customs agency, etc.
Typically to book a pet as "manifest cargo" you will need to go through the cargo reservation line for the airline. If you call up the regular passenger reservation line and tell them you want to send a pet as cargo they can usually give you the number or transfer you.
You can still be on the same flight as your pet in most cases. The difference will also be that you will check your pet in at the cargo area (sometimes an entirely different part of the airport) versus the regular check-in area at the passenger terminal. This can add to the logistical work of trying to fly with your pet. Additionally, most cargo shipments have "cut-off" times of about 2-4 hours prior -- this is when the cargo (your pet) must be checked-in by.
When you book a piece of cargo, it will fly on an "air way bill." This is like the tracking number essentially, and a piece of paper with that number on it with a description of the goods and the name of the consignee. Only the person who is listed as the consignee can pick up the pet on the receiving end. You will get a copy of the air way bill when you check your pet in for the flight. You will either need to forward this to your consignee in HK or if you are the consignee, take it with you to HK for when you clear your pet through customs.
"Accompanied/excess luggage" (or baggage) means the pet travels attached to you when you are flying as a passenger on the plane. It is usually cheaper to go this way. The pet still goes under the plane but you check the pet in at the check-in area at the passenger terminal. There is no air way bill issued because they are like another piece of luggage, and you are not consigning them to someone on the receiving end. As mentioned before, your pet cannot go into HK as excess luggage due to the HK government's regulations.
Hopefully this helps somewhat. Happy travels!!
RF