It can be confusing to hear all these terms. They are all important and all slightly different.
A user (or a visitor) is an individual out there on the internet typing away on their keyboard who is trying to visit your site.
A visit is the same as a session. Google defines a session as a group of interactions that one user takes within a given time frame on your website. Meaning whatever a user does on your website (e.g., browses pages, downloads resources, purchases products) before they leave equals one session.
SiteSpect evaluates certain characteristics about users to determine if they should be part of a Campaign. This is called assignment.
Counting happens when SiteSpect determines that the user has been exposed to a change or Variation.