Why is there only a vaccine for military personnel but not the general public?

Level of risk. Vaccines are recommended for people at risk for certain diseases, most take 2-4 weeks to work. Military personnel are at far greater risk, due to the nature of their work, for certain diseases. Thusly they are immunized against diseases we don't experience in the USA. This is particularly true for personnel on 'mobility' ie mobilized to the far reaches of the planet on a moment's notice.
Which vaccine are. You referring to? Some vaccinations are mission required. Without know what you are specifically referring to - can't give a very specific answer.
Which vaccine? The only one that I can think of recently was the smallpox vaccine. This was a common vaccine prior to 1972, but routine use was stopped at that time due to eradication of the disease worldwide. Post-9/11 there were concerns about the use of the virus (it"s still stored in some labs) in bioterrorism, leading to vaccinating some of the military. Some severe side effects limited its use.