A reship is when you live outside of the US, and the reship company gives you a US address to ship the items to. Once the items are delivered to the reship address, you can then ship it out again to wherever you live. This is for stores that don't ship to your country.
AFAIK, a drop is basically using another address that is not yours. For example, you buy the items and send it to your neighbors address. Once the item gets delivered, you take the package and refund it. If the company does bill you, it won't go to your address, and will go to your neighbor's, and since the name doesn't exist under the neighbor's address, no one gets billed.