In any given FIXED population, there are several responses to an infection.
Group A will get the infection and either will be cured, or survive and develop antibodies - they have immunity
Group B will get a vaccine if it is available and will develop antibodies - they have immunity
Group C will neither get the infection and for what ever reason, do not receive the vaccine - they are NOT immune
Group D will be those in group A or B who loose their immunity - they are NOT immune.
Now remember, we are deal only with a FIXED population. In this scenario if there are enough people in groups A & B and a small enough percent of the population in C & D, then the government / scientist / medical personnel CLAIM herd immunity. Understand that no actual immunity is provided to groups C & D. If they are exposed, because they have no immunity, they can get the illness.
Further, the population is no longer fixed at a local or even national level. People travel and someone who is a carrier can and often does, travel into the population bringing the illness back into play. Witness the recent outbreaks of childhood illnesses that were brought back to the US during the recent illegal migration from Latin America, even after having achieved herd immunity.
So if we have achieved herd immunity, say well into the 90+ percent, there are still those who can and will get the illness - they are NOT immune. They are relying on a lack of exposure to the illness. If someone exposes them, they are just as likely to get sick as before the so called herd immunity.
I know how this works all too well. As a child, I was contra indicated for the small pox vaccine due to a skin condition. During my school years, my district would put out a notice to all of us that could not receive all of our vaccines. I had to ... every year ... reaffirm that I could not receive the vaccine and that I was still not vaccinated.
When I joined the Army at 18, my skin condition had subsided and I was able to get the vaccine then. I am very pro voluntary vaccine. I have traveled the world with my job and I have been vaccinated against just about everything except Japanese Encephalitis.
My point is simply this. The term herd immunity is used by the government as a subtle manipulation and is an attempt to get everyone vaccinated.