When you get vaccinated, and are exposed to covid for example, does covid initially infect some cells, and then your body quicky resolves it before you come infectious and have any symptoms? if so,does this act as another "booster" and raise antibody?

The COVID-19 vaccines are not live vaccines like MMR, Varicella, rotavirus, or influenza (intranasal). Moderna/Pfizer contain mRNA to help our body identify the spike proteins on the surface of the coronavirus. The J&J vaccine uses an adenovirus DNA vector in a different way to the same effect: to identify the spike proteins. If you get exposed, your immune system will be able to mount a response

Covid uses the spike protein as the key to get into the human cell when we are exposed the the virus. The mRNA vaccine (Pfizer or Moderna) helps our body to produce anti spike protein antibody so it neutralizes the spike protein and the virus loses the key to enter our cell. With infection, your body will act like you have a booster but you also develop different Ab besides anti spike protein Ab.

COVID-19 infection results in much wider array of bodily immune reactions, as contrasted to the vaccines involves IgA in the upper respiratory airways (nose, sinuses). Very clear that the natural infection will confer immunity lasting far longer than the vaccine effect. But the combination of both infection and vaccine seems to provide the best protection of all, as effects are additive.