Just came across this thread on a search, and just wanted to chime in.
There's no one meaning for "long form" or "short form" when it comes to birth certificates. However, the most common meaning for "long form" is one that is made from a image of the original archived document, complete with images of the original signatures of the parent(s), certifier, and registrar. A short form most often means an "abstract" that more often than not includes the names of the parents. These days, most abstracts are computer-generated from databases, but in the past they could have been transcribed by typewriter and then certified by the registrar as accurate. However, I've heard of some places that have detailed database forms that they call "long forms". It's like a whole page of information, including parents names, place of birth, etc.
The State Dept now requires that at least one parent's name be on the birth certificate for a routine first-time passport issuance. That wasn't always a given. Some states/counties issued birth certificates without all this info.
Some states issue only abstracts (Hawaii). Others only issue an image of the original (California). Others will produce a "long form" image on request, but issue the abstract for normal business - like Texas.
As for using one on a closed-loop cruise as a US-born US citizen, there really is no difference in terms of acceptance for this purpose. They just want a certified copy complete with an official seal of some sort.
However, I'd just recommend getting a passport. Saves all the hassle of not having the right document. There are literally thousands of different forms issued by different cities, counties, and states that may differ in ways that might mean it won't be accepted. Getting a passport gets that out of the way. If there's an issue, it can be handled well before the trip.