I'll take a swing at this, being an infectious disease epidemiologist.
When people talk about the "effectiveness of the vaccine", what's actually happening is that they're talking about a smear of different things, which is why you're (justifiably) confused.
There's a few different aspects to think about:
1) When people say things like "The Moderna vaccine is 95% effective", the statistic they're citing is that in a clinical trial, the participants in the treatment arm of the trial had 5% of the outcomes the study was tracking as compared to the treatment arm. In the case of the early vaccine trials, this is stuff like...well...death or severe disease requiring ICU treatment.
It importantly does not mean you have a 5% chance if you get COVID. You have 5% of whatever the chance of someone who didn't have the vaccine has.
There's a reason that endpoint was chosen. A few actually. First, it's the most important one from a public health standpoint, in terms of immediately addressing the pandemic. It's also straightforward and unambiguous to study, which paves the way for faster licensing and thus getting it into the arms of the public. Studying things like if a vaccine is enough to induce herd immunity is much harder as a statistical problem.
Note that I haven't said anything about stopping the epidemic here. That's because this endpoint doesn't measure that. It's possible, for example, that the vaccine can protect you by reducing the severity of an infection, but that that would just push it to an asymptomatic infection that can be passed to others. That's why there's still public health messaging about wearing a mask even if you're vaccinated, etc.
2) There are follow up studies, which are still being done (and for which we are starting to get results) about whether or not the vaccine also reduces whether or not you can give the virus to others. This is what most people think of when we think about vaccines.
3) We don't know how long it will last, but it's likely fairly long lasting, and this is something that we can (and are) monitoring to make sure people don't need booster shots, etc.
4) Herd immunity depends on point #2 working well, and being at a fairly high level. One thing to keep in mind that I say a lot is that "herd immunity" is about a specific place at a specific point in time. It's possible for example that a city or town can have high enough vaccine levels to have achieved herd immunity, but the country (or the globe...) not being vaccinated enough for SARS-CoV-2 to have "gone away".
Public health thinks about this using a couple terms:
Control - "We've got a handle on this, but we've still got it"
Elimination - "This is gone in our area, but could come back"
Eradication - "This is gone forever"
TB is an example of a disease the U.S. has under Control. This is what we're aiming for with COVID-19 right now. Measles, Mumps and Rubella are, in most of the U.S., considered Eliminated. Smallpox is Eradicated.